Question

The midpoint m and one endpoint a are given. find the coordinates of the other endpoint.

A(4, -2) and M(1/2, 0)

Answer 1

Coordinates of Midpoint, knowing A(x₁, y₁) and B(x₂, y₂) is

x(of midpoint) = (x₁+x₂)÷2
y(of midpoint) = (y₁+y₂)÷2

Let A(4, -2) be one end point and B(x₂, y₂) , the other end point. Moreover the coordinate of the midpoint are given= M(1/2, 0)


1) x(of midpoint) = (x₁+x₂)÷2 = (4+x₂)÷2 , but x(of midpoint) = 1/2
Then 1/2 = (4+x₂)÷2 and x₂ = -3

2) y(of midpoint) = (y₁+y₂)÷2 = (-2+y₂)÷2 , but y(of midpoint) = 0
Then 0 = (-2+y₂)÷2 and y₂ = 2

Hence the pair of the other end is B(-3,2)