Calculators / Geometry / Midpoint

Midpoint Calculator

Published on: September 22, 2024

This Midpoint Calculator helps you find the point exactly halfway between two points on a coordinate plane. It uses the formula M = ((x₁ + x₂)/2, (y₁ + y₂)/2), where (x₁, y₁) and (x₂, y₂) are the two points. Add the x-coordinates and divide by 2, then add the y-coordinates and divide by 2 to get the midpoint. It is a simple way to check answers, understand the midpoint formula, and practise basic geometry step by step.
Line with midpoint labeled M
Enter your coordinates below.

Step-by-step method

  1. Identify what is given.
  2. Write the midpoint formula.
  3. Substitute the values and compute the midpoint coordinates.

Formula:

M = ((x₁ + x₂)/2, (y₁ + y₂)/2)

Example 1: (x₁, y₁)=(0, 0), (x₂, y₂)=(6, 4)

Step 1 - Identify what is given.

In this problem: The given points are (0, 0) and (6, 4).

(x₁, y₁)=(0, 0),(x₂, y₂)=(6, 4)

Step 2 - Write the midpoint formula.

In this problem: Use the midpoint formula: M = ((x₁ + x₂)/2, (y₁ + y₂)/2).

M=((x₁ + x₂)/2, (y₁ + y₂)/2)

Step 3 - Substitute the values and compute the midpoint coordinates.

In this problem: Substitute the values: M = ((0 + 6)/2, (0 + 4)/2) = (6/2, 4/2) = (3, 2).

M=((0+6)/2, (0+4)/2)=(6/2, 4/2)=(3, 2)

Final answer: M = (3, 2)

Example 2: (x₁, y₁)=(-2, 5), (x₂, y₂)=(8, 1)

Step 1 - Identify what is given.

In this problem: The given points are (-2, 5) and (8, 1).

(x₁, y₁)=(-2, 5),(x₂, y₂)=(8, 1)

Step 2 - Write the midpoint formula.

In this problem: Use the midpoint formula: M = ((x₁ + x₂)/2, (y₁ + y₂)/2).

M=((x₁ + x₂)/2, (y₁ + y₂)/2)

Step 3 - Substitute the values and compute the midpoint coordinates.

In this problem: Substitute the values: M = ((-2 + 8)/2, (5 + 1)/2) = (6/2, 6/2) = (3, 3).

M=((-2+8)/2, (5+1)/2)=(6/2, 6/2)=(3, 3)

Final answer: M = (3, 3)