Question

A segment in the complex plane has a midpoint at −1 + 7i. If one endpoint of the segment is at

3 + 8i, what is the other endpoint?
__+__i

Answer 1

-5, 6i

Explanation:

Answer 2

Consider two pairs of coordinates (x₁, y₁) and (x₂, y₂), the mid-point of these coordinates are
`( (x_1+x_2)/(2) , (y_1+y_2)/(2) )`

We have midpoint (-1, 7i) and one pair of coordinate (3, 8i)

The other pair of coordinate would be given by

`( (x_1+3)/(2)= -1, (y_1+8)/(2) =7)`

The value of x is (2 × -1) - 3 = -2 - 3 = -5
The value of y is (2 × 7) - 8 = 14 - 8 = 6

The value of x represents the real part
The value of y represents the imaginary part

The other coordinate is (-5, 6i)