Question

Find the perimeter of FOX with vertices F(-3,2), O(5,-1), and X(-1,-4).

Answer 1

You have to find the perimeter of the figure FOX

Given the points F(-3,2), O(5,-1) and X(-1,-4)

The first step is to plot the figure

You have to determine the side lengths of the triangle, to calculate the side lengths you can use the following formula:

$d=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2}$

Where

d is the distance between two points on the coordinate system

(x₁,y₁) are the coordinates of one of the points

(x₂,y₂) are the coordinates of the second point.

Side FO

F(-3,2)

O(5,-1)

$\begin{gathered} FO=\sqrt[]{(5-(-3))^2+(2-(-1))^2} \\ FO=\sqrt[]{(5+3)^2+(2+1)^2} \\ FO=\sqrt[]{(8)^2+(3)^2} \\ FO=\sqrt[]{73} \end{gathered}$

Side OX

O(5,-1)

X(-1,-4)

$\begin{gathered} OX=\sqrt[]{(5-(-1))^2+(-1-(-4))^2} \\ OX=\sqrt[]{(5+1)^2+(-1+4)^2} \\ OX=\sqrt[]{(6)^2+(3)^2} \\ OX=\sqrt[]{45} \\ OX=3\sqrt[]{5} \end{gathered}$

Side XF

X=(-1,-4)

F=(-3,2)

$\begin{gathered} XF=\sqrt[]{(-1-(-3))^2+(2-(-4))^2} \\ XF=\sqrt[]{(-1+3)^2+(2+4)^2} \\ XF=\sqrt[]{(2)^2+(6)^2} \\ XF=\sqrt[]{40} \\ XF=2\sqrt[]{10} \end{gathered}$

So the side lengths of the triangle are:

FO=√73

OX=3√5

XF=2√10

The perimeter can be calculated as the sum of the lengths of the sides of the figures

$\begin{gathered} P=FO+OX+XF \\ P=\sqrt[]{73}+3\sqrt[]{5}+2\sqrt[]{10} \\ P=21.576\cong21.58 \end{gathered}$