Question

For the coordinates of P and M (the midpoint) are given. Find the coordinates for Q.

P(-2, 3) and M (5, 1)

Answer 1

Given an endpoint and a midpoint, to look for the other endpoint, the midpoint formula is merely manipulated. The average of the x-coordinates for P and Q have to equate to the x-coordinate of M. The same is applied to the y-coordinates. This is shown below:

X-coordinates:

(-2 + Qx)/2 = 5
(-2 + Qx) = 10

Qx = 12

Y-coordinates:

(3 + Qy)/2 = 1
3 + Qy = 2

Qy = -1

Therefore, Q has the coordinates (12 , -1)