Draw z₁, z₂ and the locus in an Argand diagram.

01 / Standard#Your turn

z_1=3+5i,\quad z_2=5+i,\quad|z-z_1|=|z-z_2|

Official paper · jm02-2022 · 4(a)(ii) · PDF 6

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Real and imaginary parts are horizontal and vertical coordinates.

Hint 2

The locus line has equation y=x/2+1.

Worked solution

Plot the two fixed points.
$z_1\leftrightarrow(3,5),\quad z_2\leftrightarrow(5,1)$
Draw the entire line through the midpoint (4,3) with slope 1/2.
$y=x/2+1,\quad x\in\mathbb R$

The marked points and full perpendicular-bisector line are shown.

Checks and common pitfalls: The locus is a line, not merely the segment between the plotted endpoints.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Plot the two fixed points.
$z_1\leftrightarrow(3,5),\quad z_2\leftrightarrow(5,1)$
Draw the entire line through the midpoint (4,3) with slope 1/2.
$y=x/2+1,\quad x\in\mathbb R$

Think first. Reveal a hint when the class is ready.

2022 JM02