g10-08-06 · Syllabus supplement
Translate a midpoint and a distance
What changes when both endpoints receive the same translation?
1 MIN · PREDICT ON PAPER
Translate A=(−1,0),B=(3,2) by(2,1); predict the new midpoint and distance.
Discuss or write first. No typed answer is required to continue.
The midpoint translates once; the distance remains fixed.
2 MIN · EXPLAIN AND REVISE
Which condition does your claim need?
Compare at least two cases. Write a reason, then check the explanation together.
Reveal explanation and conditions
A common translation preserves endpoint differences and distance. The midpoint receives the same translation as the endpoints.
Conditions: Distance uses the Euclidean metric with the same unit on both axes; coincident endpoints have distance0.
Mathematical justification: M=(A+B)/2, so M′=((A+t)+(B+t))/2=M+t; B′−A′=B−A gives unchanged distance.
1 MIN · EXIT CHECK
Find the midpoint of(−1,0),(3,2), then translate it by(2,1).
Check after answering
Midpoint(1,1); translated midpoint(3,2).
Teacher guidance and extension
Before: Coordinates, displacement and Pythagoras.
Ask: Why is the translation added once after dividing the sum by2?
Watch for: Adding the translation twice when calculating the midpoint.
Challenge: Check whether doubling all coordinates is a translation.
Suggested timing: predict 1 min, compare 3 min, explain 2 min, exit check 1 min. Observations can suggest a claim; they do not prove it for every input.
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