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:
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.
This page was written by Stephen Clarke.
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