Question

A segment has a midpoint at (2,-7) and an endpoint at (8,-5). What are the coordinates of the other endpoint?

Answer 1

Answer:

(-4,-9)

Step-by-step explanation:

Given a segment AB with endpoints with coordinates

A: $(x_A,y_A)$

B: $(x_B,y_B)$

The coordinates of the midpoint M of the segment AB are given by:

$x_M = x_A + \frac{x_B-x_A}{2}\\y_M = y_A + \frac{y_B-y_A}{2}$ (1)

In this problem, we know that:

- The midpoint of the segment AB has coordinates

$x_M=2\\y_M=-7$

- One of the endpoint of the segment has coordinates

$x_B=8\\y_B=-5$

So we  can find the coordinates of the other endpoint A by re-arranging eq.(1) above:

$x_A=2x_M-x_B\\y_A=2y_M-y_B$

And substituting, we find:

$x_A=2(2)-8=-4\\y_A=2(-7)-(-5)=-9$

So, the coordinates of the other endpoint are (-4,-9).