Question

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

P(3, 11) and M (0, 0)

Answer 1

Given an endpoint of a segment and a midpoint, the other endpoint can be obtained by manipulation of the midpoint formula. The said formula is shown below:

Let: (a,b) = coordinates of point 1 ; (c,d) = coordinates of point 2; (e,f) = coordinates of the midpoint

Midpoint = ( (a+c)/2 , (b + d)/2 )

From the formula: (a+c)/2 = e ; (b + d)/2 = f

Since we are already given an endpoint and the midpoint, we can solve for the other endpoint using the obtained equations. This is shown below:

(a+c)/2 = e
(3 + c)/2 = 0
c = -3

(b + d)/2 = f
(11 + d)/2 = 0
d = -11

Therefore, the coordinates of the other point is Q(-3,-11)