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)?
Reflect the endpoint around the midpoint.
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.
#8#in the positive x direction from M:
#0 + 8 = 8#
#4#in the positive y direction from M:
#3 + 4 = 7#
So the other endpoint is