Question

question 1 of 13, step 1 of 1
0/15
correct
find the perimeter of the triangle whose vertices are (-1,2), (-1,4), and (-4, - 1). write the exact answer. do not round.
answer

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 distance between $(-1,2)$ and $(-1,4)$

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

Step3: Calculate distance between $(-1,4)$ and $(-4,-1)$

Let $(x_1,y_1)=(-1,4)$ and $(x_2,y_2)=(-4,-1)$. Then $d_2=\sqrt{(-4-(-1))^2+(-1 - 4)^2}=\sqrt{(-3)^2+(-5)^2}=\sqrt{9 + 25}=\sqrt{34}$.

Step4: Calculate distance between $(-4,-1)$ and $(-1,2)$

Let $(x_1,y_1)=(-4,-1)$ and $(x_2,y_2)=(-1,2)$. Then $d_3=\sqrt{(-1-(-4))^2+(2 - (-1))^2}=\sqrt{(3)^2+(3)^2}=\sqrt{9+9}=\sqrt{18}=3\sqrt{2}$.

Step5: Calculate perimeter

The perimeter $P=d_1 + d_2 + d_3=2+\sqrt{34}+3\sqrt{2}$.

Answer:

$2+\sqrt{34}+3\sqrt{2}$