Use the lesson question here for paper discussion; the original activity opens separately.
Worked example1
Find the reflection of A=(-3,2) in the y-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Identify the y-axis before changing a sign.
Change only the first coordinate.
The image is (3,2); verify the distance to the axis.
Reflection in the y-axis negates x and keeps y.
Apply the rule to (-3,2) to obtain (3,2).
The original point and its image are equally far from the axis on opposite sides, unless they lie on it.
Reference answer
A′=(3,2).
Use the labelled axes and unit grid.
Check your work
Keep the coordinate parallel to the axis and change the perpendicular one.
Give an ordered pair in the original x,y order.
Guided attempt2
Construct the reflection of the whole triangle ABC in the y-axis. Reflect every vertex, then join the images in the same order.
Use the labelled axes and unit grid.
The given axis is the y-axis; do not construct a new axis.
Reflect A, B and C separately before joining anything.
Check that each joining segment to its image is perpendicular to, and bisected by, the axis.
For each vertex, draw the perpendicular to the given axis and preserve its distance on the opposite side.
The image vertices are A′=(4,1), B′=(1,1), C′=(2,4).
Join A′B′, B′C′ and C′A′. A reflection preserves lengths and angles.
Reference answer
A′=(4,1); B′=(1,1); C′=(2,4).
Use the labelled axes and unit grid.
Check your work
Reflect all vertices and preserve their order.
Show a complete reflected figure, not only one image point.
Prerequisite3
Find the reflection of A=(4,0) in the x-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Identify the x-axis before changing a sign.
Change only the second coordinate.
The image is (4,0); verify the distance to the axis.
Reflection in the x-axis keeps x and negates y.
Apply the rule to (4,0) to obtain (4,0).
The original point and its image are equally far from the axis on opposite sides, unless they lie on it.
Reference answer
A′=(4,0).
Use the labelled axes and unit grid.
Check your work
Keep the coordinate parallel to the axis and change the perpendicular one.
Give an ordered pair in the original x,y order.
Prerequisite4
Find the reflection of A=(-2,-3) in the x-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Identify the x-axis before changing a sign.
Change only the second coordinate.
The image is (-2,3); verify the distance to the axis.
Reflection in the x-axis keeps x and negates y.
Apply the rule to (-2,-3) to obtain (-2,3).
The original point and its image are equally far from the axis on opposite sides, unless they lie on it.
Reference answer
A′=(-2,3).
Use the labelled axes and unit grid.
Check your work
Keep the coordinate parallel to the axis and change the perpendicular one.
Give an ordered pair in the original x,y order.
Independent practice5
Find the reflection of A=(3,-4) in the x-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Identify the x-axis before changing a sign.
Change only the second coordinate.
The image is (3,4); verify the distance to the axis.
Reflection in the x-axis keeps x and negates y.
Apply the rule to (3,-4) to obtain (3,4).
The original point and its image are equally far from the axis on opposite sides, unless they lie on it.
Reference answer
A′=(3,4).
Use the labelled axes and unit grid.
Check your work
Keep the coordinate parallel to the axis and change the perpendicular one.
Give an ordered pair in the original x,y order.
Independent practice6
Find the reflection of A=(-5,2) in the y-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Identify the y-axis before changing a sign.
Change only the first coordinate.
The image is (5,2); verify the distance to the axis.
Reflection in the y-axis negates x and keeps y.
Apply the rule to (-5,2) to obtain (5,2).
The original point and its image are equally far from the axis on opposite sides, unless they lie on it.
Reference answer
A′=(5,2).
Use the labelled axes and unit grid.
Check your work
Keep the coordinate parallel to the axis and change the perpendicular one.
Give an ordered pair in the original x,y order.
Independent practice7
Construct the reflection of the whole triangle ABC in the x-axis. Reflect every vertex, then join the images in the same order.
Use the labelled axes and unit grid.
The given axis is the x-axis; do not construct a new axis.
Reflect A, B and C separately before joining anything.
Check that each joining segment to its image is perpendicular to, and bisected by, the axis.
For each vertex, draw the perpendicular to the given axis and preserve its distance on the opposite side.
The image vertices are A′=(-4,-1), B′=(-1,-1), C′=(-2,-4).
Join A′B′, B′C′ and C′A′. A reflection preserves lengths and angles.
Reference answer
A′=(-4,-1); B′=(-1,-1); C′=(-2,-4).
Use the labelled axes and unit grid.
Check your work
Reflect all vertices and preserve their order.
Show a complete reflected figure, not only one image point.
Independent practice8
Find the reflection of A=(0,-4) in the y-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Identify the y-axis before changing a sign.
Change only the first coordinate.
The image is (0,-4); verify the distance to the axis.
Reflection in the y-axis negates x and keeps y.
Apply the rule to (0,-4) to obtain (0,-4).
The original point and its image are equally far from the axis on opposite sides, unless they lie on it.
Reference answer
A′=(0,-4).
Use the labelled axes and unit grid.
Check your work
Keep the coordinate parallel to the axis and change the perpendicular one.
Give an ordered pair in the original x,y order.
Exit question9
Find the reflection of A=(2,3) in the x-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Identify the x-axis before changing a sign.
Change only the second coordinate.
The image is (2,-3); verify the distance to the axis.
Reflection in the x-axis keeps x and negates y.
Apply the rule to (2,3) to obtain (2,-3).
The original point and its image are equally far from the axis on opposite sides, unless they lie on it.
Reference answer
A′=(2,-3).
Use the labelled axes and unit grid.
Check your work
Keep the coordinate parallel to the axis and change the perpendicular one.
Give an ordered pair in the original x,y order.
Exit question10
Find the reflection of A=(-3,0) in the x-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Identify the x-axis before changing a sign.
Change only the second coordinate.
The image is (-3,0); verify the distance to the axis.
Reflection in the x-axis keeps x and negates y.
Apply the rule to (-3,0) to obtain (-3,0).
The original point and its image are equally far from the axis on opposite sides, unless they lie on it.
Reference answer
A′=(-3,0).
Use the labelled axes and unit grid.
Check your work
Keep the coordinate parallel to the axis and change the perpendicular one.
Give an ordered pair in the original x,y order.
Further practice11
Find the reflection of A=(-4,-2) in the y-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Identify the y-axis before changing a sign.
Change only the first coordinate.
The image is (4,-2); verify the distance to the axis.
Reflection in the y-axis negates x and keeps y.
Apply the rule to (-4,-2) to obtain (4,-2).
The original point and its image are equally far from the axis on opposite sides, unless they lie on it.
Reference answer
A′=(4,-2).
Use the labelled axes and unit grid.
Check your work
Keep the coordinate parallel to the axis and change the perpendicular one.
Give an ordered pair in the original x,y order.
Further practice12
Find the reflection of A=(1,5) in the x-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Identify the x-axis before changing a sign.
Change only the second coordinate.
The image is (1,-5); verify the distance to the axis.
Reflection in the x-axis keeps x and negates y.
Apply the rule to (1,5) to obtain (1,-5).
The original point and its image are equally far from the axis on opposite sides, unless they lie on it.
Reference answer
A′=(1,-5).
Use the labelled axes and unit grid.
Check your work
Keep the coordinate parallel to the axis and change the perpendicular one.
Give an ordered pair in the original x,y order.
Further practice13
Construct the reflection of the whole triangle ABC in the y-axis. Reflect every vertex, then join the images in the same order.
Use the labelled axes and unit grid.
The given axis is the y-axis; do not construct a new axis.
Reflect A, B and C separately before joining anything.
Check that each joining segment to its image is perpendicular to, and bisected by, the axis.
For each vertex, draw the perpendicular to the given axis and preserve its distance on the opposite side.
The image vertices are A′=(4,1), B′=(1,1), C′=(2,4).
Join A′B′, B′C′ and C′A′. A reflection preserves lengths and angles.
Reference answer
A′=(4,1); B′=(1,1); C′=(2,4).
Use the labelled axes and unit grid.
Check your work
Reflect all vertices and preserve their order.
Show a complete reflected figure, not only one image point.
Further practice14
Find the reflection of A=(0,0) in the y-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Identify the y-axis before changing a sign.
Change only the first coordinate.
The image is (0,0); verify the distance to the axis.
Reflection in the y-axis negates x and keeps y.
Apply the rule to (0,0) to obtain (0,0).
The original point and its image are equally far from the axis on opposite sides, unless they lie on it.
Reference answer
A′=(0,0).
Use the labelled axes and unit grid.
Check your work
Keep the coordinate parallel to the axis and change the perpendicular one.
Give an ordered pair in the original x,y order.
Extension15
First reflect A=(3,2) in the x-axis, obtaining B=(3,−2). Now reflect B in the y-axis. Find the final point C.
Use the labelled axes and unit grid.
Identify the y-axis before changing a sign.
Change only the first coordinate.
The image is (-3,-2); verify the distance to the axis.
Reflection in the y-axis negates x and keeps y.
Apply the rule to (3,-2) to obtain (-3,-2).
The original point and its image are equally far from the axis on opposite sides, unless they lie on it.
Reference answer
C=(−3,−2).
Use the labelled axes and unit grid.
Check your work
Keep the coordinate parallel to the axis and change the perpendicular one.
Give an ordered pair in the original x,y order.
Extension16
Construct the reflection of the whole triangle ABC in the x-axis. Reflect every vertex, then join the images in the same order.
Use the labelled axes and unit grid.
The given axis is the x-axis; do not construct a new axis.
Reflect A, B and C separately before joining anything.
Check that each joining segment to its image is perpendicular to, and bisected by, the axis.
For each vertex, draw the perpendicular to the given axis and preserve its distance on the opposite side.
The image vertices are A′=(-4,-1), B′=(-1,-1), C′=(-2,-4).
Join A′B′, B′C′ and C′A′. A reflection preserves lengths and angles.
Reference answer
A′=(-4,-1); B′=(-1,-1); C′=(-2,-4).
Use the labelled axes and unit grid.
Check your work
Reflect all vertices and preserve their order.
Show a complete reflected figure, not only one image point.
Preparation and assessment notes
Prerequisites
Perpendicular bisectors, ordered pairs and the coordinate axes.
Look for in students’ work
Use the worked model and guided attempt selectively, then the eight core questions. Keep further practice and extensions optional. Ask for a reason and an original-equation or expansion check.
Collect the paper exit questions and note completion and common errors. This page does not grade or store paper answers.
All reference answers
Worked example1
Find the reflection of A=(-3,2) in the y-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Reference answer
A′=(3,2).
Reflection in the y-axis negates x and keeps y.
Apply the rule to (-3,2) to obtain (3,2).
The original point and its image are equally far from the axis on opposite sides, unless they lie on it.
Keep the coordinate parallel to the axis and change the perpendicular one.
Give an ordered pair in the original x,y order.
Use the labelled axes and unit grid.
Guided attempt2
Construct the reflection of the whole triangle ABC in the y-axis. Reflect every vertex, then join the images in the same order.
Use the labelled axes and unit grid.
Reference answer
A′=(4,1); B′=(1,1); C′=(2,4).
For each vertex, draw the perpendicular to the given axis and preserve its distance on the opposite side.
The image vertices are A′=(4,1), B′=(1,1), C′=(2,4).
Join A′B′, B′C′ and C′A′. A reflection preserves lengths and angles.
Reflect all vertices and preserve their order.
Show a complete reflected figure, not only one image point.
Use the labelled axes and unit grid.
Prerequisite3
Find the reflection of A=(4,0) in the x-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Reference answer
A′=(4,0).
Reflection in the x-axis keeps x and negates y.
Apply the rule to (4,0) to obtain (4,0).
The original point and its image are equally far from the axis on opposite sides, unless they lie on it.
Keep the coordinate parallel to the axis and change the perpendicular one.
Give an ordered pair in the original x,y order.
Use the labelled axes and unit grid.
Prerequisite4
Find the reflection of A=(-2,-3) in the x-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Reference answer
A′=(-2,3).
Reflection in the x-axis keeps x and negates y.
Apply the rule to (-2,-3) to obtain (-2,3).
The original point and its image are equally far from the axis on opposite sides, unless they lie on it.
Keep the coordinate parallel to the axis and change the perpendicular one.
Give an ordered pair in the original x,y order.
Use the labelled axes and unit grid.
Independent practice5
Find the reflection of A=(3,-4) in the x-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Reference answer
A′=(3,4).
Reflection in the x-axis keeps x and negates y.
Apply the rule to (3,-4) to obtain (3,4).
The original point and its image are equally far from the axis on opposite sides, unless they lie on it.
Keep the coordinate parallel to the axis and change the perpendicular one.
Give an ordered pair in the original x,y order.
Use the labelled axes and unit grid.
Independent practice6
Find the reflection of A=(-5,2) in the y-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Reference answer
A′=(5,2).
Reflection in the y-axis negates x and keeps y.
Apply the rule to (-5,2) to obtain (5,2).
The original point and its image are equally far from the axis on opposite sides, unless they lie on it.
Keep the coordinate parallel to the axis and change the perpendicular one.
Give an ordered pair in the original x,y order.
Use the labelled axes and unit grid.
Independent practice7
Construct the reflection of the whole triangle ABC in the x-axis. Reflect every vertex, then join the images in the same order.
Use the labelled axes and unit grid.
Reference answer
A′=(-4,-1); B′=(-1,-1); C′=(-2,-4).
For each vertex, draw the perpendicular to the given axis and preserve its distance on the opposite side.
The image vertices are A′=(-4,-1), B′=(-1,-1), C′=(-2,-4).
Join A′B′, B′C′ and C′A′. A reflection preserves lengths and angles.
Reflect all vertices and preserve their order.
Show a complete reflected figure, not only one image point.
Use the labelled axes and unit grid.
Independent practice8
Find the reflection of A=(0,-4) in the y-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Reference answer
A′=(0,-4).
Reflection in the y-axis negates x and keeps y.
Apply the rule to (0,-4) to obtain (0,-4).
The original point and its image are equally far from the axis on opposite sides, unless they lie on it.
Keep the coordinate parallel to the axis and change the perpendicular one.
Give an ordered pair in the original x,y order.
Use the labelled axes and unit grid.
Exit question9
Find the reflection of A=(2,3) in the x-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Reference answer
A′=(2,-3).
Reflection in the x-axis keeps x and negates y.
Apply the rule to (2,3) to obtain (2,-3).
The original point and its image are equally far from the axis on opposite sides, unless they lie on it.
Keep the coordinate parallel to the axis and change the perpendicular one.
Give an ordered pair in the original x,y order.
Use the labelled axes and unit grid.
Exit question10
Find the reflection of A=(-3,0) in the x-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Reference answer
A′=(-3,0).
Reflection in the x-axis keeps x and negates y.
Apply the rule to (-3,0) to obtain (-3,0).
The original point and its image are equally far from the axis on opposite sides, unless they lie on it.
Keep the coordinate parallel to the axis and change the perpendicular one.
Give an ordered pair in the original x,y order.
Use the labelled axes and unit grid.
Further practice11
Find the reflection of A=(-4,-2) in the y-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Reference answer
A′=(4,-2).
Reflection in the y-axis negates x and keeps y.
Apply the rule to (-4,-2) to obtain (4,-2).
The original point and its image are equally far from the axis on opposite sides, unless they lie on it.
Keep the coordinate parallel to the axis and change the perpendicular one.
Give an ordered pair in the original x,y order.
Use the labelled axes and unit grid.
Further practice12
Find the reflection of A=(1,5) in the x-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Reference answer
A′=(1,-5).
Reflection in the x-axis keeps x and negates y.
Apply the rule to (1,5) to obtain (1,-5).
The original point and its image are equally far from the axis on opposite sides, unless they lie on it.
Keep the coordinate parallel to the axis and change the perpendicular one.
Give an ordered pair in the original x,y order.
Use the labelled axes and unit grid.
Further practice13
Construct the reflection of the whole triangle ABC in the y-axis. Reflect every vertex, then join the images in the same order.
Use the labelled axes and unit grid.
Reference answer
A′=(4,1); B′=(1,1); C′=(2,4).
For each vertex, draw the perpendicular to the given axis and preserve its distance on the opposite side.
The image vertices are A′=(4,1), B′=(1,1), C′=(2,4).
Join A′B′, B′C′ and C′A′. A reflection preserves lengths and angles.
Reflect all vertices and preserve their order.
Show a complete reflected figure, not only one image point.
Use the labelled axes and unit grid.
Further practice14
Find the reflection of A=(0,0) in the y-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Reference answer
A′=(0,0).
Reflection in the y-axis negates x and keeps y.
Apply the rule to (0,0) to obtain (0,0).
The original point and its image are equally far from the axis on opposite sides, unless they lie on it.
Keep the coordinate parallel to the axis and change the perpendicular one.
Give an ordered pair in the original x,y order.
Use the labelled axes and unit grid.
Extension15
First reflect A=(3,2) in the x-axis, obtaining B=(3,−2). Now reflect B in the y-axis. Find the final point C.
Use the labelled axes and unit grid.
Reference answer
C=(−3,−2).
Reflection in the y-axis negates x and keeps y.
Apply the rule to (3,-2) to obtain (-3,-2).
The original point and its image are equally far from the axis on opposite sides, unless they lie on it.
Keep the coordinate parallel to the axis and change the perpendicular one.
Give an ordered pair in the original x,y order.
Use the labelled axes and unit grid.
Extension16
Construct the reflection of the whole triangle ABC in the x-axis. Reflect every vertex, then join the images in the same order.
Use the labelled axes and unit grid.
Reference answer
A′=(-4,-1); B′=(-1,-1); C′=(-2,-4).
For each vertex, draw the perpendicular to the given axis and preserve its distance on the opposite side.
The image vertices are A′=(-4,-1), B′=(-1,-1), C′=(-2,-4).
Join A′B′, B′C′ and C′A′. A reflection preserves lengths and angles.
Reflect all vertices and preserve their order.
Show a complete reflected figure, not only one image point.
All 53 Year 7–8 upper- and lower-volume packs in Traditional Chinese and English. Includes teacher answers; student core, further practice and teacher papers are in separate folders.
Core student worksheet: two A4 pages. Further practice is separate. Teacher copies include reference reasoning.
Textbook reference and authorship
Chapter-core practice after the mapped textbook lessons; these tasks do not replace every first-teaching period.
大湾区初中数学三维课堂（八年级上册）正文.pdf
Year 8, upper volume · text pp. 35–38 · foundation lessons 18–19
Original questions and explanations; the source textbook and answer PDFs are not reproduced here.
Reflecting whole figures and coordinates
Year 8, upper volume · text pp. 35–38 · foundation lessons 18–19 · 1/2
Name: __________ Class: ______ Date: __________
Worked example1
Find the reflection of A=(-3,2) in the y-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Guided attempt2
Construct the reflection of the whole triangle ABC in the y-axis. Reflect every vertex, then join the images in the same order.
Use the labelled axes and unit grid.
Prerequisite3
Find the reflection of A=(4,0) in the x-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Prerequisite4
Find the reflection of A=(-2,-3) in the x-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Reflecting whole figures and coordinates
Year 8, upper volume · text pp. 35–38 · foundation lessons 18–19 · 2/2
Name: __________ Class: ______ Date: __________
Independent practice5
Find the reflection of A=(3,-4) in the x-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Independent practice6
Find the reflection of A=(-5,2) in the y-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Independent practice7
Construct the reflection of the whole triangle ABC in the x-axis. Reflect every vertex, then join the images in the same order.
Use the labelled axes and unit grid.
Independent practice8
Find the reflection of A=(0,-4) in the y-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Exit question9
Find the reflection of A=(2,3) in the x-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Exit question10
Find the reflection of A=(-3,0) in the x-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Reflecting whole figures and coordinates — Further practice
Year 8, upper volume · text pp. 35–38 · foundation lessons 18–19
Further practice11
Find the reflection of A=(-4,-2) in the y-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Further practice12
Find the reflection of A=(1,5) in the x-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Further practice13
Construct the reflection of the whole triangle ABC in the y-axis. Reflect every vertex, then join the images in the same order.
Use the labelled axes and unit grid.
Further practice14
Find the reflection of A=(0,0) in the y-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Extension15
First reflect A=(3,2) in the x-axis, obtaining B=(3,−2). Now reflect B in the y-axis. Find the final point C.
Use the labelled axes and unit grid.
Extension16
Construct the reflection of the whole triangle ABC in the x-axis. Reflect every vertex, then join the images in the same order.
Use the labelled axes and unit grid.
Reflecting whole figures and coordinates — Teacher answers
Year 8, upper volume · text pp. 35–38 · foundation lessons 18–19
Use the worked model and guided attempt selectively, then the eight core questions. Keep further practice and extensions optional. Ask for a reason and an original-equation or expansion check.
Worked example1
Find the reflection of A=(-3,2) in the y-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Reference answer
A′=(3,2).
Reflection in the y-axis negates x and keeps y.
Apply the rule to (-3,2) to obtain (3,2).
The original point and its image are equally far from the axis on opposite sides, unless they lie on it.
Keep the coordinate parallel to the axis and change the perpendicular one.
Give an ordered pair in the original x,y order.
Use the labelled axes and unit grid.
Guided attempt2
Construct the reflection of the whole triangle ABC in the y-axis. Reflect every vertex, then join the images in the same order.
Use the labelled axes and unit grid.
Reference answer
A′=(4,1); B′=(1,1); C′=(2,4).
For each vertex, draw the perpendicular to the given axis and preserve its distance on the opposite side.
The image vertices are A′=(4,1), B′=(1,1), C′=(2,4).
Join A′B′, B′C′ and C′A′. A reflection preserves lengths and angles.
Reflect all vertices and preserve their order.
Show a complete reflected figure, not only one image point.
Use the labelled axes and unit grid.
Prerequisite3
Find the reflection of A=(4,0) in the x-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Reference answer
A′=(4,0).
Reflection in the x-axis keeps x and negates y.
Apply the rule to (4,0) to obtain (4,0).
The original point and its image are equally far from the axis on opposite sides, unless they lie on it.
Keep the coordinate parallel to the axis and change the perpendicular one.
Give an ordered pair in the original x,y order.
Use the labelled axes and unit grid.
Prerequisite4
Find the reflection of A=(-2,-3) in the x-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Reference answer
A′=(-2,3).
Reflection in the x-axis keeps x and negates y.
Apply the rule to (-2,-3) to obtain (-2,3).
The original point and its image are equally far from the axis on opposite sides, unless they lie on it.
Keep the coordinate parallel to the axis and change the perpendicular one.
Give an ordered pair in the original x,y order.
Use the labelled axes and unit grid.
Independent practice5
Find the reflection of A=(3,-4) in the x-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Reference answer
A′=(3,4).
Reflection in the x-axis keeps x and negates y.
Apply the rule to (3,-4) to obtain (3,4).
The original point and its image are equally far from the axis on opposite sides, unless they lie on it.
Keep the coordinate parallel to the axis and change the perpendicular one.
Give an ordered pair in the original x,y order.
Use the labelled axes and unit grid.
Independent practice6
Find the reflection of A=(-5,2) in the y-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Reference answer
A′=(5,2).
Reflection in the y-axis negates x and keeps y.
Apply the rule to (-5,2) to obtain (5,2).
The original point and its image are equally far from the axis on opposite sides, unless they lie on it.
Keep the coordinate parallel to the axis and change the perpendicular one.
Give an ordered pair in the original x,y order.
Use the labelled axes and unit grid.
Independent practice7
Construct the reflection of the whole triangle ABC in the x-axis. Reflect every vertex, then join the images in the same order.
Use the labelled axes and unit grid.
Reference answer
A′=(-4,-1); B′=(-1,-1); C′=(-2,-4).
For each vertex, draw the perpendicular to the given axis and preserve its distance on the opposite side.
The image vertices are A′=(-4,-1), B′=(-1,-1), C′=(-2,-4).
Join A′B′, B′C′ and C′A′. A reflection preserves lengths and angles.
Reflect all vertices and preserve their order.
Show a complete reflected figure, not only one image point.
Use the labelled axes and unit grid.
Independent practice8
Find the reflection of A=(0,-4) in the y-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Reference answer
A′=(0,-4).
Reflection in the y-axis negates x and keeps y.
Apply the rule to (0,-4) to obtain (0,-4).
The original point and its image are equally far from the axis on opposite sides, unless they lie on it.
Keep the coordinate parallel to the axis and change the perpendicular one.
Give an ordered pair in the original x,y order.
Use the labelled axes and unit grid.
Exit question9
Find the reflection of A=(2,3) in the x-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Reference answer
A′=(2,-3).
Reflection in the x-axis keeps x and negates y.
Apply the rule to (2,3) to obtain (2,-3).
The original point and its image are equally far from the axis on opposite sides, unless they lie on it.
Keep the coordinate parallel to the axis and change the perpendicular one.
Give an ordered pair in the original x,y order.
Use the labelled axes and unit grid.
Exit question10
Find the reflection of A=(-3,0) in the x-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Reference answer
A′=(-3,0).
Reflection in the x-axis keeps x and negates y.
Apply the rule to (-3,0) to obtain (-3,0).
The original point and its image are equally far from the axis on opposite sides, unless they lie on it.
Keep the coordinate parallel to the axis and change the perpendicular one.
Give an ordered pair in the original x,y order.
Use the labelled axes and unit grid.
Further practice11
Find the reflection of A=(-4,-2) in the y-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Reference answer
A′=(4,-2).
Reflection in the y-axis negates x and keeps y.
Apply the rule to (-4,-2) to obtain (4,-2).
The original point and its image are equally far from the axis on opposite sides, unless they lie on it.
Keep the coordinate parallel to the axis and change the perpendicular one.
Give an ordered pair in the original x,y order.
Use the labelled axes and unit grid.
Further practice12
Find the reflection of A=(1,5) in the x-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Reference answer
A′=(1,-5).
Reflection in the x-axis keeps x and negates y.
Apply the rule to (1,5) to obtain (1,-5).
The original point and its image are equally far from the axis on opposite sides, unless they lie on it.
Keep the coordinate parallel to the axis and change the perpendicular one.
Give an ordered pair in the original x,y order.
Use the labelled axes and unit grid.
Further practice13
Construct the reflection of the whole triangle ABC in the y-axis. Reflect every vertex, then join the images in the same order.
Use the labelled axes and unit grid.
Reference answer
A′=(4,1); B′=(1,1); C′=(2,4).
For each vertex, draw the perpendicular to the given axis and preserve its distance on the opposite side.
The image vertices are A′=(4,1), B′=(1,1), C′=(2,4).
Join A′B′, B′C′ and C′A′. A reflection preserves lengths and angles.
Reflect all vertices and preserve their order.
Show a complete reflected figure, not only one image point.
Use the labelled axes and unit grid.
Further practice14
Find the reflection of A=(0,0) in the y-axis. Explain which coordinate changes.
Use the labelled axes and unit grid.
Reference answer
A′=(0,0).
Reflection in the y-axis negates x and keeps y.
Apply the rule to (0,0) to obtain (0,0).
The original point and its image are equally far from the axis on opposite sides, unless they lie on it.
Keep the coordinate parallel to the axis and change the perpendicular one.
Give an ordered pair in the original x,y order.
Use the labelled axes and unit grid.
Extension15
First reflect A=(3,2) in the x-axis, obtaining B=(3,−2). Now reflect B in the y-axis. Find the final point C.
Use the labelled axes and unit grid.
Reference answer
C=(−3,−2).
Reflection in the y-axis negates x and keeps y.
Apply the rule to (3,-2) to obtain (-3,-2).
The original point and its image are equally far from the axis on opposite sides, unless they lie on it.
Keep the coordinate parallel to the axis and change the perpendicular one.
Give an ordered pair in the original x,y order.
Use the labelled axes and unit grid.
Extension16
Construct the reflection of the whole triangle ABC in the x-axis. Reflect every vertex, then join the images in the same order.
Use the labelled axes and unit grid.
Reference answer
A′=(-4,-1); B′=(-1,-1); C′=(-2,-4).
For each vertex, draw the perpendicular to the given axis and preserve its distance on the opposite side.
The image vertices are A′=(-4,-1), B′=(-1,-1), C′=(-2,-4).
Join A′B′, B′C′ and C′A′. A reflection preserves lengths and angles.
Reflect all vertices and preserve their order.
Show a complete reflected figure, not only one image point.
