Question

find the perimeter of the triangle whose vertices are (-1, -6), (5, -6), and (5, 2). write the exact answer. do not round.

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Calculate length of first - side

Let $(x_1,y_1)=(-1,-6)$ and $(x_2,y_2)=(5,-6)$. Then $d_1=\sqrt{(5 - (-1))^2+(-6-(-6))^2}=\sqrt{(5 + 1)^2+(0)^2}=\sqrt{36}=6$.

Step3: Calculate length of second - side

Let $(x_1,y_1)=(5,-6)$ and $(x_2,y_2)=(5,2)$. Then $d_2=\sqrt{(5 - 5)^2+(2-(-6))^2}=\sqrt{(0)^2+(8)^2}=\sqrt{64}=8$.

Step4: Calculate length of third - side

Let $(x_1,y_1)=(-1,-6)$ and $(x_2,y_2)=(5,2)$. Then $d_3=\sqrt{(5 - (-1))^2+(2-(-6))^2}=\sqrt{(5 + 1)^2+(8)^2}=\sqrt{36 + 64}=\sqrt{100}=10$.

Step5: Calculate perimeter

The perimeter $P$ of a triangle is $P=d_1 + d_2 + d_3$. So $P=6 + 8+10 = 24$.

Answer:

24