﻿ Distance Between Points; the Midpoint Formula

# Distance Between Points; the Midpoint Formula

## The Distance Formula

To find the distance between any two points in a coordinate plane:

• Subtract the $x$-values in any order; square the result.
• Subtract the $y$-values in any order; square the result.
• Add together the previous two quantities.
• Take the square root of the result.

This sequence of operations is expressed in the Distance Formula:

the Distance Formula

The distance between points $\,(x_1,y_1)\,$ and $\,(x_2,y_2)\,$ is given by the Distance Formula:

$$\cssId{s10}{\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}}$$

For a complete review of the distance between two points in the coordinate plane, study the following lesson, which includes a derivation, a discussion of subscript notation, and examples:   The Distance Formula.

## The Midpoint Formula

To find the midpoint of the line segment between any two points in a coordinate plane:

• Average the $x$-values of the two pointsthat is, add them and divide by $2\,.$ This gives the $x$-value of the midpoint.
• Average the $y$-values of the two pointsthat is, add them and divide by $2\,.$ This gives the $y$-value of the midpoint.

This sequence of operations is expressed in the Midpoint Formula:

THE MIDPOINT FORMULA

The midpoint of the line segment between points $\,(x_1,y_1)\,$ and $\,(x_2,y_2)\,$ is given by the Midpoint Formula:

$$\cssId{s25}{\left( \frac{x_1+x_2}2,\frac{y_1+y_2}2 \right)}$$

For a complete review of midpoints, including a derivation and examples, study:   The Midpoint Formula.