Question

1. the coordinates of triangle pqr plotted on a coordinate plane are p (-6,9), q (6,4), and r (2,1). enter a number in the box to complete the sentence. the perimeter of the triangle is units. round your answer to the nearest tenth.

Explanation:

Step1: Use distance formula for PQ

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For points $P(-6,9)$ and $Q(6,4)$, we have $x_1=-6,y_1 = 9,x_2=6,y_2 = 4$. Then $PQ=\sqrt{(6-(-6))^2+(4 - 9)^2}=\sqrt{(12)^2+(-5)^2}=\sqrt{144 + 25}=\sqrt{169}=13$.

Step2: Use distance formula for QR

For points $Q(6,4)$ and $R(2,1)$, $x_1=6,y_1 = 4,x_2=2,y_2 = 1$. Then $QR=\sqrt{(2 - 6)^2+(1 - 4)^2}=\sqrt{(-4)^2+(-3)^2}=\sqrt{16+9}=\sqrt{25}=5$.

Step3: Use distance formula for RP

For points $R(2,1)$ and $P(-6,9)$, $x_1=2,y_1 = 1,x_2=-6,y_2 = 9$. Then $RP=\sqrt{(-6 - 2)^2+(9 - 1)^2}=\sqrt{(-8)^2+(8)^2}=\sqrt{64 + 64}=\sqrt{128}=8\sqrt{2}\approx11.3$.

Step4: Calculate perimeter

The perimeter $P$ of triangle $PQR$ is $P=PQ + QR+RP$. So $P=13 + 5+11.3=29.3$.

Answer:

$29.3$