Question

question 3 of 13, step 1 of 1
2/15
correct
find the perimeter of the triangle whose vertices are (-1, - 8), (4, - 8), and (4, 4). write the exact answer. do not round.
answer

Explanation:

Step1: Use distance formula for side 1

Let $(x_1,y_1)=(-1,-8)$ and $(x_2,y_2)=(4,-8)$. The distance formula is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Since $y_1 = y_2$, $d_1=\sqrt{(4 - (-1))^2+(-8+8)^2}=\sqrt{5^2+0^2}=5$.

Step2: Use distance formula for side 2

Let $(x_1,y_1)=(4,-8)$ and $(x_2,y_2)=(4,4)$. Since $x_1 = x_2$, $d_2=\sqrt{(4 - 4)^2+(4 + 8)^2}=\sqrt{0^2+12^2}=12$.

Step3: Use distance formula for side 3

Let $(x_1,y_1)=(-1,-8)$ and $(x_2,y_2)=(4,4)$. $d_3=\sqrt{(4+1)^2+(4 + 8)^2}=\sqrt{5^2+12^2}=\sqrt{25 + 144}=\sqrt{169}=13$.

Step4: Calculate perimeter

The perimeter $P=d_1 + d_2 + d_3$. So $P=5+12+13 = 30$.

Answer:

30