Midpoint Formula

In this lesson, we will learn

• the midpoint formula.
• how to find the midpoint given two endpoints.
• how to find one endpoint given the midpoint and another endpoint.
• how to proof the midpoint formula.

The Midpoint Formula

Some coordinate geometry questions may require you to find the midpoint of line segments in the coordinate plane. To find a point that is halfway between two given points, get the average of the x-values and the average of the y-values.

The midpoint between the two points (x₁,y₁) and (x₂,y₂) is given by the formula

For example:

The midpoint of the points A(1,4) and B(5,6) is

Find the midpoint given two endpoints

We can use the midpoint formula to find the midpoint when given two endpoints.

Example:
Find the midpoint of the two points A(1, -3) and B(4, 5).

Solution:
Midpoint = = (2.5, 1)

Worksheet 1, Worksheet 2 to calculate the midpoint.

This video gives the formula for finding the midpoint of two points and does one example to find the midpoint.

Find an endpoint when given a midpoint and another endpoint

We can use the midpoint formula to find an endpoint when given a midpoint and another endpoint.

Example:
M(3, 8) is the midpoint of the line AB. A has the coordinates (-2, 3), Find the coordinates of B.

Solution:
Let the coordinates of B be (x, y)

Coordinates of B = (8, 13)

The following video gives an example of finding a missing endpoint if given the midpoint and another endpoint.

Proof of the Midpoint Formula

We can use the Pythagorean theorem to proof the midpoint formula.

The following video gives a proof of the midpoint formula using the Pythagorean Theorem.

Custom Search

© Copyright 2005, 2012 - onlinemathlearning.com
Embedded content, if any, are copyrights of their respective owners.