Question

23 select the correct answer. a triangle has vertices (-1, 2), (3, 1), and (7, 2). what is the approximate perimeter of the triangle? round your answer to the nearest hundredth. a. 16 units b. 16.24 units c. 16.31 units d. 17 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 $(x_1,y_1)=(-1,2)$ and $(x_2,y_2)=(3,1)$.
$d_1=\sqrt{(3 - (-1))^2+(1 - 2)^2}=\sqrt{4^2+( - 1)^2}=\sqrt{16 + 1}=\sqrt{17}\approx4.123$.

Step3: Calculate side 2

Let $(x_1,y_1)=(3,1)$ and $(x_2,y_2)=(7,2)$.
$d_2=\sqrt{(7 - 3)^2+(2 - 1)^2}=\sqrt{4^2+1^2}=\sqrt{16 + 1}=\sqrt{17}\approx4.123$.

Step4: Calculate side 3

Let $(x_1,y_1)=(-1,2)$ and $(x_2,y_2)=(7,2)$.
$d_3=\sqrt{(7 - (-1))^2+(2 - 2)^2}=\sqrt{8^2+0^2}=8$.

Step5: Calculate perimeter

$P=d_1 + d_2 + d_3\approx4.123+4.123 + 8=16.246\approx16.25$.

Answer:

B. 16.24 units