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QuizMultiple Choice

Distance and Midpoints in the Complex Plane

Question 1 • *PGHS Precalculus B

A circle has center at –6 + 2i and a point on the circle at 4 + 26i. Which of the following points is also on the circle?

Answer
A
–19 + 15i
B
–16 – 22i
C
6 + 16i
D
20 – 24i

Explanation

The radius is the distance from the center (−6, 2) to the point (4, 26): the horizontal and vertical differences are 10 and 24, so the radius squared is 10² + 24² = 676. For choice B, (−16, −22), the differences from the center are −10 and −24, giving (−10)² + (−24)² = 676. Thus choice B, −16 − 22i, is also on the circle.

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