Question

1. triangle abc is shown below. a(-2,-2) b(1,2) c(1,-6) what is the perimeter of triangle abc? a. 12 b. 24 c. 18 d. 32

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 $AB$

For $A(-2,-2)$ and $B(1,2)$, $x_1=-2,y_1 = - 2,x_2=1,y_2 = 2$. Then $AB=\sqrt{(1-(-2))^2+(2 - (-2))^2}=\sqrt{(3)^2+(4)^2}=\sqrt{9 + 16}=\sqrt{25}=5$.

Step3: Calculate length of $BC$

For $B(1,2)$ and $C(1,-6)$, $x_1=1,y_1 = 2,x_2=1,y_2=-6$. Then $BC=\sqrt{(1 - 1)^2+(-6 - 2)^2}=\sqrt{0+( - 8)^2}=\sqrt{64}=8$.

Step4: Calculate length of $AC$

For $A(-2,-2)$ and $C(1,-6)$, $x_1=-2,y_1=-2,x_2=1,y_2=-6$. Then $AC=\sqrt{(1-(-2))^2+(-6 - (-2))^2}=\sqrt{(3)^2+(-4)^2}=\sqrt{9 + 16}=\sqrt{25}=5$.

Step5: Calculate perimeter

The perimeter $P$ of $\triangle ABC$ is $P=AB + BC+AC=5 + 8+5=18$.

Answer:

C. 18