Midpoint Formula Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Midpoint Formula.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

A formula for finding the point exactly halfway between two points in the coordinate plane, by averaging their coordinates.

Finding the midpoint is like finding the average position. If two friends live at different addresses on the same street, the midpoint is the house number exactly halfway between them—the average of their two house numbers. In 2D, you just average both coordinates independently.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: The midpoint is the average of the two endpoints—average the x's, average the y's.

Common stuck point: The midpoint formula finds the point that is equidistant from both endpoints along the segment.

Worked Examples

Example 1

easy
Find the midpoint of the segment joining (2, 8) and (6, 4).

Solution

  1. 1
    The midpoint of a segment is the average of the two endpoints' coordinates: M = \left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}\right). Averaging 'splits the difference' equally.
  2. 2
    Identify the endpoints: (x_1, y_1) = (2, 8) and (x_2, y_2) = (6, 4). Compute the averages separately for x and y.
  3. 3
    Substitute: M = \left(\frac{2+6}{2},\, \frac{8+4}{2}\right) = \left(\frac{8}{2},\, \frac{12}{2}\right) = (4, 6). Verify: the point (4,6) lies exactly halfway between (2,8) and (6,4) — the distance from (2,8) to (4,6) equals the distance from (4,6) to (6,4) (both equal \sqrt{8}).

Answer

M = (4, 6)
The midpoint is simply the average of the x-coordinates and the average of the y-coordinates. It represents the exact centre of the line segment.

Example 2

medium
The midpoint of segment PQ is M(3, -1). If P = (-2, 4), find the coordinates of Q.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Find the midpoint of the segment joining (-5, 3) and (7, -1).

Example 2

easy
A circle has diameter endpoints A(-6, 2) and B(4, 10). Find the coordinates of the centre of the circle.
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Background Knowledge

These ideas may be useful before you work through the harder examples.

coordinate planeadditiondivision