# How do you find the coordinates of the other endpoint of a segment with the given endpoint T(-8,-1) and midpoint M(0,3)?

Jun 15, 2017

Reflect the endpoint around the midpoint.

#### Explanation:

To do this algebraically, you consider how to get to the midpoint from the endpoint, and then do that move again to get to the other endpoint.

In the x direction, to get from T to M, you need to go $8$ in the positive direction.

In the y direction, to get from T to M, you need to go $4$ in the positive direction.

Therefore, to get to our other endpoint (let's call it E), we need to make these same moves again.

Move $8$ in the positive x direction from M:

$0 + 8 = 8$

Move $4$ in the positive y direction from M:

$3 + 4 = 7$

So the other endpoint is $\left(8 , 7\right)$. The following image shows this process graphically: