Question

A line segment has an endpoint at (-4,8) and a midpoint

at (2,-2) what is the x coordinate of the other endpoint?

Answer 1

The coordinates of the midpoints are the average coordinates of the endpoints. Suppose (x1,y1) and (x2,y2) are the endpoints and (xm,ym) is the midpoint, we have xm=x1+x22 and ym=y1+y22 . Therefore, 2xm=x1+x2 and 2ym=y1+y2 . From there, we should be able to figure the other endpoint out given an endpoint and the midpoint.