Question

the points n(-3,1), q(-3,-7), and p(1,-5) form a triangle. plot the points then click the \graph triangle\ button. then find the perimeter of the triangle. round your answer to the nearest tenth if necessary. click on the graph to plot a point. click a point to delete it.

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 NQ

For points $N(-3,1)$ and $Q(-3,-7)$, $x_1=-3,y_1 = 1,x_2=-3,y_2=-7$. Then $d_{NQ}=\sqrt{(-3+3)^2+(-7 - 1)^2}=\sqrt{0+( - 8)^2}=8$.

Step3: Calculate length of QP

For points $Q(-3,-7)$ and $P(1,-5)$, $x_1=-3,y_1=-7,x_2 = 1,y_2=-5$. Then $d_{QP}=\sqrt{(1 + 3)^2+(-5 + 7)^2}=\sqrt{4^2+2^2}=\sqrt{16 + 4}=\sqrt{20}=2\sqrt{5}\approx4.5$.

Step4: Calculate length of PN

For points $P(1,-5)$ and $N(-3,1)$, $x_1=1,y_1=-5,x_2=-3,y_2 = 1$. Then $d_{PN}=\sqrt{(-3 - 1)^2+(1 + 5)^2}=\sqrt{(-4)^2+6^2}=\sqrt{16+36}=\sqrt{52}=2\sqrt{13}\approx7.2$.

Step5: Calculate perimeter

The perimeter $P=d_{NQ}+d_{QP}+d_{PN}=8 + 2\sqrt{5}+2\sqrt{13}\approx8+4.5+7.2 = 19.7$.

Answer:

$19.7$