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?

The Distance Formula is the equation you use if you are trying to find the distance between two points on a graph, or two given points. It can also be used to tell what type of triangle or shape is on a graph etc. To use the Distance Formula you need to know two points on a line and plug in the points in the equation (below this text box).
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Example of how to use the Distance Formula

Your given points A and B, A(-2,1) and B(1,5) and you want to know how far away they are from each other. how do i do this?

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

When telling what triangle you are working with, you have to know the three types of triangles and how to determine them.

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

If you have a triangle who has the points A(0,0) B(0,2) and C(3,0) and want to know what type of triangle it is you need to use the distance formula. First you need to find the distance of each line, (AB), (BC), (CA), use the distance formula and find the lengths between these line segments.

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

If you have a triangle who has the points A(0,0) B(1,3) C(2,0) and want to know what type of triangle it is, you need to do the same as last time use the distance formula to do it, if youve forgotten refer to the formula above.

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.

Videos

Here are some videos to help you remember the distance formula and how to use it. :)
Distance Formula Song Memory Device
Distance Formula Song