The Midpoint Formula

The purpose of the midpoint formula

• The midpoint formula is used to find the midpoint or the halfway point of a line segment or between two points

What is the midpoint formula?

How to apply the midpoint formula

• Example – find midpoint of the line segment with endpoints (0,-4) and (8,6)

Solution to example

x₁ = 0, x₂ = 8, y₁ = -4, and y₂ = 6

(8 + 0 / 2, -4 + 6 /2) = (4/2, 2/2) = (2,1)

• So, the midpoint is (2, 1)

For you to try

• Find the midpoint of the line segment with endpoints (-7,-3) and (11,-1)

Solution x₁ = -7, x₂ = 11, y₁ = -3, y₂ = -1

(-7 + 11 /2, -3 + -1 /2) = (4/2, -4/2) = (2,-2)

• So, the midpoint is (2, -2)

What if you’re given the midpoint and an endpoint and are asked to find the other endpoint…

• Example – find the other endpoint of the line segment with endpoint (10,2) and midpoint (-3,-2).

Solution to example

We know that according to the midpoint formula (10 + x₂) /2 = -3 and

(2 + y₂) /2 = -2, so we must solve both equations.

2 (10 + x₂)/2 = -3 2∙ ∙ 10 + x₂ = -6 -10 -10 x₂ = -16

Solution to example continued

• (2 + y₂) /2 = -2 2 (2 + y₂) /2 = -2 2∙ ∙ 2 + y₂ = -4 -2 -2 y₂ = -6So, the other endpoint is (-

16, -6)

For you to try

• Find the endpoint of the line segment with one endpoint (0, -9) and the midpoint (5, 8).