Question

Endpoint: (-9,-1), midpoint: (8,14) given the midpoint and one endpoint of a line segment, find the other endpoint.

Answer 1

(25, 29)

Explanation:

The midpoint formula can be solved to give an expression for one end point of a line segment in terms of the other end point and the midpoint.

Formula

The midpoint (M) of segment AB is found from ...

M = (A +B)/2

Solving for B, we get ...

B = 2M -A

Application

For A(-9, -1) and M(8, 14), we find the end point B to be ...

B = 2(8, 14) -(-9, -1)

B = (16 -(-9), 28 -(-1)) = (25, 29)

The other end point is (25, 29.