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Midpoint of a Line Segment

Objective Learn the algebraic formula for the midpoint of a line segment, whose endpoints are given by ordered pairs of numbers.

This is a relatively straightforward lesson, which shows that the x- and y-coordinates of the midpoint of a line segment can be obtained by taking the averages of the x- and y-coordinates, respectively.

Begin by reembering the formula for the average of two numbers x and y.

Take a look at the following diagram.

The average is the midpoint of the segment between the two points, or the halfway point between x and y.

Two points in a plane have coordinates (x 0 , y 0) and (x 1 , y 1). How can we find the coordinates of the midpoint of the segment joining them?

For two points in a plane, the halfway point between them should have an x-coordinate that is halfway between the x-coordinates of the two points. This is shown in the diagram below.

In the same way, the y-coordinate of the midpoint is the midpoint of the y-coordinates. The formula for the y-coordinate of the midpoint is . This is shown in the diagram below.

The formula for the coordinates of the midpoint of a line segment is given below.

Definition of Midpoint

The midpoint of the segment joining two points at (x 0 , y 0) and (x 1 , y 1) is given by

Now you should practice using the formula to find midpoints of line segments.

Exercises

Find the coordinates of the midpoint of a segment with each pair of endpoints.

1. A (9, 4), B (7, 6) (8, 5)

2. L (8, -2), M (0, 10) (4, 4)

3. X (2, 5), Y ( -6, 3) ( -2, 4)

4. T (1, -9), U (4, 7) (2.5, -1)