Midpoint Calculator

Published on: September 22, 2024
Final Answer: Free • Full Steps: Plus

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 formula.
  3. Substitute the values and calculate the midpoint.

Formula:

\(M = \left(\tfrac{x_{1} + x_{2}}{2}, \tfrac{y_{1} + y_{2}}{2}\right)\)

Example 1:

\((x_{1}, y_{1}) = (0, 0),\; (x_{2}, y_{2}) = (6, 4)\)

Step 1 - Identify what is given.

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

\((x_{1}, y_{1}) = (0, 0),\; (x_{2}, y_{2}) = (6, 4)\)

Step 2 - Write the formula.

In this problem: Use the midpoint formula: \(M = \left(\tfrac{x_{1} + x_{2}}{2}, \tfrac{y_{1} + y_{2}}{2}\right)\).

\(M = \left(\tfrac{x_{1} + x_{2}}{2}, \tfrac{y_{1} + y_{2}}{2}\right)\)

Step 3 - Substitute the values and calculate the midpoint.

In this problem: Substitute the values: \(M = \left(\tfrac{0 + 6}{2}, \tfrac{0 + 4}{2}\right) = \left(\tfrac{6}{2}, \tfrac{4}{2}\right) = (3, 2)\).

\(M = \left(\tfrac{0 + 6}{2}, \tfrac{0 + 4}{2}\right) = \left(\tfrac{6}{2}, \tfrac{4}{2}\right) = (3, 2)\)

Final answer:

\(M = (3, 2)\)

Example 2:

\((x_{1}, y_{1}) = (-2, 5),\; (x_{2}, y_{2}) = (8, 1)\)

Step 1 - Identify what is given.

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

\((x_{1}, y_{1}) = (-2, 5),\; (x_{2}, y_{2}) = (8, 1)\)

Step 2 - Write the formula.

In this problem: Use the midpoint formula: \(M = \left(\tfrac{x_{1} + x_{2}}{2}, \tfrac{y_{1} + y_{2}}{2}\right)\).

\(M = \left(\tfrac{x_{1} + x_{2}}{2}, \tfrac{y_{1} + y_{2}}{2}\right)\)

Step 3 - Substitute the values and calculate the midpoint.

In this problem: Substitute the values: \(M = \left(\tfrac{-2 + 8}{2}, \tfrac{5 + 1}{2}\right) = \left(\tfrac{6}{2}, \tfrac{6}{2}\right) = (3, 3)\).

\(M = \left(\tfrac{-2 + 8}{2}, \tfrac{5 + 1}{2}\right) = \left(\tfrac{6}{2}, \tfrac{6}{2}\right) = (3, 3)\)

Final answer:

\(M = (3, 3)\)