Question

find the perimeter of the triangle whose vertices are (-4, - 3), (8, - 3), and (8, 2). write the exact answer. do not round.

Explanation:

Step1: Use distance formula for side 1

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For points $(-4,-3)$ and $(8,-3)$, $x_1=-4,y_1 = - 3,x_2=8,y_2=-3$. Then $d_1=\sqrt{(8 - (-4))^2+(-3-(-3))^2}=\sqrt{(8 + 4)^2+(0)^2}=\sqrt{144}=12$.

Step2: Use distance formula for side 2

For points $(8,-3)$ and $(8,2)$, $x_1 = 8,y_1=-3,x_2=8,y_2 = 2$. Then $d_2=\sqrt{(8 - 8)^2+(2-(-3))^2}=\sqrt{(0)^2+(5)^2}=5$.

Step3: Use distance formula for side 3

For points $(-4,-3)$ and $(8,2)$, $x_1=-4,y_1=-3,x_2=8,y_2 = 2$. Then $d_3=\sqrt{(8-(-4))^2+(2 - (-3))^2}=\sqrt{(8 + 4)^2+(2 + 3)^2}=\sqrt{144 + 25}=\sqrt{169}=13$.

Step4: Calculate perimeter

The perimeter $P$ of a triangle is $P=d_1 + d_2+d_3$. So $P=12 + 5+13=30$.

Answer:

$30$