Question

find the perimeter of the triangle defined by the coordinates (7, 1), (-6, 1), and (10, 6). (round to nearest tenth)
a 32.6 units
b 33.6 units
c 34.6 units
d 35.6 units

Explanation:

Step1: Use 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

Let $(x_1,y_1)=(7,1)$ and $(x_2,y_2)=(-6,1)$. Then $d_1=\sqrt{(-6 - 7)^2+(1 - 1)^2}=\sqrt{(-13)^2+0^2}=13$.

Step3: Calculate side 2

Let $(x_1,y_1)=(-6,1)$ and $(x_2,y_2)=(10,6)$. Then $d_2=\sqrt{(10+6)^2+(6 - 1)^2}=\sqrt{16^2+5^2}=\sqrt{256 + 25}=\sqrt{281}\approx16.8$.

Step4: Calculate side 3

Let $(x_1,y_1)=(10,6)$ and $(x_2,y_2)=(7,1)$. Then $d_3=\sqrt{(7 - 10)^2+(1 - 6)^2}=\sqrt{(-3)^2+(-5)^2}=\sqrt{9 + 25}=\sqrt{34}\approx5.8$.

Step5: Calculate perimeter

$P=d_1 + d_2+d_3=13+16.8+5.8 = 35.6$.

Answer:

D. 35.6 units