How to Find the Midpoint

Finding the Midpoint

The midpoint is half way between two points.

We can find the Cartesian coordinates of the midpoint if we know the Cartesian coordinates of the two points.

Imagine we wanted to find the midpoint between the points with Cartesian coordinates (1, 2) and (5, 4). The image below shows what we mean by the midpoint:

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How to Find the Midpoint

Finding the midpoint between two points is easy.

Question

Find the midpoint between the points with Cartesian coordinates (1, 2) and (5, 4).

Step-by-Step:

1

Add the x-coordinates of the two points together. The x-coordinate of (1, 2) is 1. The x-coordinate of (5, 4) is 5.

1 + 5 = 6

2

Divide the answer (6) by 2.

6 ÷ 2 = 3

3 is the x-coordinate of the midpoint.

3

Add the y-coordinates of the two points together. The y-coordinate of (1, 2) is 2. The y-coordinate of (5, 4) is 4.

2 + 4 = 6

4

Divide the answer (6) by 2.

6 ÷ 2 = 3

3 is the y-coordinate of the midpoint.

5

Write down the Cartesian coordinates of the midpoint as a pair of numbers in brackets, separated by a comma.

The x-coordinate (3) found in Step 2 goes on the left.

The y-coordinate (3) found in Step 4 goes on the right.

Answer:

How to Find the Midpoint Using a Formula

The midpoint between a point at (x1, y1) and a point at (x2, y2) is found at:

The image below shows what we mean by x1, y1, x2 and y2:

Slider

The slider below gives another example of how to find the midpoint of two points.

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See Also

What are Cartesian coordinates? What is the x-coordinate? What is the y-coordinate? What is the mean?