Question

question 8 of 13, step 1 of 1 find the perimeter of the triangle whose vertices are (4, - 2), (-4,0), and (-1, - 3). 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 side 1 length

Let $(x_1,y_1)=(4,-2)$ and $(x_2,y_2)=(-4,0)$. Then $d_1=\sqrt{(-4 - 4)^2+(0 + 2)^2}=\sqrt{(-8)^2+2^2}=\sqrt{64 + 4}=\sqrt{68}=2\sqrt{17}$.

Step3: Calculate side 2 length

Let $(x_1,y_1)=(-4,0)$ and $(x_2,y_2)=(-1,-3)$. Then $d_2=\sqrt{(-1 + 4)^2+(-3 - 0)^2}=\sqrt{3^2+(-3)^2}=\sqrt{9 + 9}=\sqrt{18}=3\sqrt{2}$.

Step4: Calculate side 3 length

Let $(x_1,y_1)=(-1,-3)$ and $(x_2,y_2)=(4,-2)$. Then $d_3=\sqrt{(4 + 1)^2+(-2 + 3)^2}=\sqrt{5^2+1^2}=\sqrt{25+1}=\sqrt{26}$.

Step5: Calculate perimeter

The perimeter $P=d_1 + d_2 + d_3=2\sqrt{17}+3\sqrt{2}+\sqrt{26}$.

Answer:

$2\sqrt{17}+3\sqrt{2}+\sqrt{26}$