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Finding the Midpoint
(KS2, Year 6)

homegraphs_and_coordinate_geometryfinding the midpoint between points
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:

midpoint

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:

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

midpoint formula graph

Lesson Slides

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

What Are Cartesian Coordinates?

Cartesian coordinates are used to describe the position of a point on a graph. Cartesian coordinates work by measuring how far across and how far up the point is from the origin.

Why Does the Method Work?

The method works because it finds the point in the middle of the two points. The x-coordinate of the midpoint is just the average of the x-coordinates of the end points. The y-coordinate of the midpoint is just the average of the y-coordinates of the end points. Remember, the average of two numbers is found by adding them together and dividing by 2. The average of two numbers is the number exactly half way between the two numbers.
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This page was written by Stephen Clarke.

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