Question

a triangle is drawn on the coordinate plane, as shown. what is the perimeter of the triangle? round your answer to the nearest whole number. enter your answer in the box. units

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 distance between $(4,6)$ and $(3, - 1)$

Let $(x_1,y_1)=(4,6)$ and $(x_2,y_2)=(3,-1)$. Then $d_1=\sqrt{(3 - 4)^2+(-1 - 6)^2}=\sqrt{(-1)^2+(-7)^2}=\sqrt{1 + 49}=\sqrt{50}\approx7.07$.

Step3: Calculate distance between $(3,-1)$ and $(8,1)$

Let $(x_1,y_1)=(3,-1)$ and $(x_2,y_2)=(8,1)$. Then $d_2=\sqrt{(8 - 3)^2+(1+1)^2}=\sqrt{5^2+2^2}=\sqrt{25 + 4}=\sqrt{29}\approx5.39$.

Step4: Calculate distance between $(8,1)$ and $(4,6)$

Let $(x_1,y_1)=(8,1)$ and $(x_2,y_2)=(4,6)$. Then $d_3=\sqrt{(4 - 8)^2+(6 - 1)^2}=\sqrt{(-4)^2+5^2}=\sqrt{16 + 25}=\sqrt{41}\approx6.40$.

Step5: Calculate perimeter

$P=d_1 + d_2 + d_3\approx7.07+5.39+6.40 = 18.86\approx19$.

Answer:

19