Distance Formula

$d(A,B)=\sqrt{(y_2-y_1{)}^2+(x_2-x_1{)}^2}$$\small\fcolorbox{#00BFFF}{white}{$d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}$}$\small\fcolorbox{#00BFFF}{white}{$d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}$}

Goal:

Find the distance between two distinct points in a coordinate plane.

Definition:

d = distance or length

A = an endpoint

B = an endpoint

Example:

Find the distance between $A(-5,2)\, and\,B(3,-2)$

Steps:

Since we know the following we can label and plug them in.

$x_1=-5$x_1=-5

$y_1 = 2$y_1 = 2

$x_2=3$x_2=3

$y_2=-2$

$d(A,B)=\small\sqrt{(\colorbox{red}{$y_2$}-\colorbox{cyan}{$y_1$})^2+(\colorbox{yellow}{$x_2$}-\colorbox{orange}{$x_1$})^2}$

$d(A,B)=\sqrt{(-2-2)^2+(3--5)^2}$

$$
$$
d(A,B)=\sqrt{(-2-2)^2+(3--5)^2}

$d(A,B)=\sqrt{(-4)^2+(8)^2}$d(A,B)=\sqrt{(-4)^2+(8)^2}

$d(A,B)=\sqrt{16+64}$d(A,B)=\sqrt{16+64}

$\colorbox{aqua}{$d(A,B)=\sqrt{80}$}$\colorbox{aqua}{$d(A,B)=\sqrt{80}$}

By: Ed

Sept. 4, 2020