Question

A segment in the complex plane has an
endpoint of 12 + 5i and a midpoint of 3 - 6i.
What is the other endpoint?
A. -6 - 17i
B. 15 - i
C. 7 - 10i
D. 9 + i

Answer 1

._____________._____________.

12 + 5i 3 - 6i ?

Let (x1,y1) = (12,5) , (x,y) = (3, -6) and (x2,y2) = ?

• By midpoint formula

x = (x1 + x2)/2 ; y = (y1 + y2)/2

3 = (12 + x2)/2 ; -6 = (5 + y2)/2

6 = 12 + x2 ; -12 = 5 + y2

6 - 12 = x2 ; -12 - 5 = y2

x2 = -6 ; -17 = y2

therefore (x,y) = (-6, -17)

•°• x + yi = -6 + (-17i) = -6 - 17i

Answer: A. -6 - 17i

Answer 2

Answer:

A.-6-17i

Step-by-step explanation:

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