For z=x+yi, derive the Cartesian equation of its locus.

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)(i) · PDF 6

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Write the two distances as square roots.

Hint 2

Square and cancel x² and y².

Worked solution

x−2y+2=0.

Checks and common pitfalls: This is the perpendicular bisector of the segment joining z₁ and z₂.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Equal distances give equal squared distances.
$(x-3)^2+(y-5)^2=(x-5)^2+(y-1)^2$
Collect the linear terms.
$4x-8y+8=0\iff x-2y+2=0$

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

2022 JM02