﻿ Review of Coordinate Geometry: the Distance Formula, the Midpoint Formula

# DISTANCE BETWEEN POINTS; THE MIDPOINT FORMULA

by Dr. Carol JVF Burns (website creator)
Follow along with the highlighted text while you listen!
• PRACTICE (online exercises and printable worksheets)

## 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

Master the ideas from this section