A segment in the complex plane has an endpoint of 12 + 5i and a midp

1.	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» ._____________._____________. 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

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»

._____________._____________.

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

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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

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