Question

find the perimeter of the triangle with vertices at (-3, 2), (1, 2), and (1, 5). round your answer to the nearest tenth, if necessary.

Explanation:

Step1: Find length of first side

Use distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ for points $(-3,2)$ and $(1,2)$. Here $x_1=-3,y_1 = 2,x_2=1,y_2 = 2$.
$d_1=\sqrt{(1-(-3))^2+(2 - 2)^2}=\sqrt{(4)^2+0^2}=4$

Step2: Find length of second side

For points $(1,2)$ and $(1,5)$, $x_1 = 1,y_1=2,x_2 = 1,y_2=5$.
$d_2=\sqrt{(1 - 1)^2+(5 - 2)^2}=\sqrt{0^2+(3)^2}=3$

Step3: Find length of third side

For points $(-3,2)$ and $(1,5)$, $x_1=-3,y_1 = 2,x_2=1,y_2 = 5$.
$d_3=\sqrt{(1-(-3))^2+(5 - 2)^2}=\sqrt{(4)^2+(3)^2}=\sqrt{16 + 9}=\sqrt{25}=5$

Step4: Calculate perimeter

Perimeter $P=d_1 + d_2+d_3$.
$P=4 + 3+5=12$

Answer:

12