AnswersPrecalculusDistance and Midpoints in the Complex Plane

Distance and Midpoints in the Complex Plane Answers

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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?

A
–19 + 15i
B
–16 – 22i
C
6 + 16i
D
20 – 24i
2
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What is the length of the radius of a circle with a center at the origin and a point on the circle at 8 + 15i?

A
i start root 7 end root
Option A
B
i start root 161 end root
Option B
C
15
D
17
3

What is the midpoint of a segment in the complex plane with endpoints at 3 – 2i and 17 – 8i?

A
StartFraction 1 over 2 EndFraction + StartFraction 9 over 2 EndFraction i
Option A
B
7 – 3i
C
10 – 5i
D
20 – 10i
4

What is the distance between 1 + 3i and 2 – 4i in the complex plane?

A
start root 10 end root
Option A
B
2 start root 10 end root
Option B
C
4i start root 3 end root
Option C
D
5 start root 2 end root
Option D
5

Joelle was asked to find the missing endpoint of a segment when given an endpoint of –6 +3i and a midpoint of –13 + i. Her work is shown below.Her mistake was

Question illustration
A
not subtracting the a and b in the original equations.
B
writing the final answer as 1+ 5i instead of 5 + i.
C
switching the endpoint and midpoint in her original equations.
D
not using –6 and 3 in one of her original equations and –13 and 1 in the other original equation.
6

What is the length of the radius of a circle with a center at 2 – i and a point on the circle at 8 + 7i?

A
2i start root 7 end root
Option A
B
start root 10 end root
Option B
C
8
D
10
7

A circle has a diameter with endpoints at 15 + 25i and –25 – 17i. Which point is also on the circle?

A
–15 +21i
B
0 + 0i
C
15 + 17i
D
16 + 24i
8

A circle has a diameter with endpoints at 5 + 18i and –3 + 2i. What is the center of the circle?

A
–11 –16i
B
1 + 10i
C
2 + 20i
D
4 + 8i
9

What is the length of the radius of a circle with a center at 2 + 3i and a point on the circle at 7 + 2i?

A
2 start root 6 end root
Option A
B
start root 26 end root
Option B
C
start root 56 end root
Option C
D
10
10

A circle has a diameter with endpoints at –3 + 18i and 7 – 6i. Which point is also on the circle?

A
–7 + 7i
B
5 + 12i
C
12 – i
D
14 + 11i

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