# Distance Formula and Applications

### MGSE9–12.G.GPE.7 Use of the distance formula.

## What is the Distance Formula and how do you use it?

## Example of how to use the Distance Formula

First you input the numbers where they belong. d=√(1-(-2))^2 + (5-1)^2

Then you solve the formula. d=√(3)^2 + (4)^2 d = √9+16.

d=√25, d=5 So the distance between the two parts is 5 units squared.

## How to determine what type of triangle it is when using the distance formula

There is the isosceles triangle, which has two equal length sides and one different length side.

the scalene triangle which has no equal length sides.

And the equilateral triangle which has all three sides the same length. In the case of the triangle on the right it is a scalene triangle.

## Example 1

the distance of line AB is 2

the line BC is 4

and line CA is 3

Since all 3 of the lines have 3 different lengths that are not the same this means this triangle is a scalene triangle.

## Example 2

You need to find the distance of each line just like last time, (AB), (BC), (CA).

the distance of line AB is 3

line BC is also 3

line CA is 2.

Since 2 of the lines have the same length and one is different that means this triangle is a isosceles.