Question

question 12 of 13, step 1 of 1
find the perimeter of the triangle whose vertices are (-1,8), (-1,6), and (-4, - 1). 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 the first - side length

Let $(x_1,y_1)=(-1,8)$ and $(x_2,y_2)=(-1,6)$. Then $d_1=\sqrt{(-1 + 1)^2+(6 - 8)^2}=\sqrt{0+( - 2)^2}=\sqrt{4}=2$.

Step3: Calculate the second - side length

Let $(x_1,y_1)=(-1,6)$ and $(x_2,y_2)=(-4,-1)$. Then $d_2=\sqrt{(-4 + 1)^2+(-1 - 6)^2}=\sqrt{(-3)^2+(-7)^2}=\sqrt{9 + 49}=\sqrt{58}$.

Step4: Calculate the third - side length

Let $(x_1,y_1)=(-4,-1)$ and $(x_2,y_2)=(-1,8)$. Then $d_3=\sqrt{(-1 + 4)^2+(8 + 1)^2}=\sqrt{3^2+9^2}=\sqrt{9+81}=\sqrt{90}=3\sqrt{10}$.

Step5: Calculate the perimeter

The perimeter $P$ of the triangle is $P=d_1 + d_2 + d_3=2+\sqrt{58}+3\sqrt{10}$.

Answer:

$2+\sqrt{58}+3\sqrt{10}$