Line segment AB has a midpoint of M. The coordinates of A are (-3, 6) and the coordinates of M are (-7,8). What are the coordinates of B?

Answer 1

Hi Boop Y.,

The midpoint formula is: midpt.(x, y) = [(x₁ + x₂)/2, (y₁ + y₂)/2] which we can use to find point B.

We are given endpoint A = (x₁, y₁) = (-3, 6) and midpoint M = (x, y) = (-7, 8). So point B = (x₂, y₂), which we will solve for.

Plugging the points into the formula: (-7, 8) = [(-3 + x₂)/2, (6 + y₂)/2] we see that:

-7 = (-3 + x₂)/2 and 8 = (6 + y₂)/2.

We can now solve for B(x₂, y₂):

-14 = -3 + x₂ and 16 = 6 + y₂

-11 = x₂ ... and... 10 = y₂

Therefore B(x₂, y₂) = (-11, 10)

I hope this helps, Joe.