Question

question: the points q(-1,5), r(-1,-4), and s(5,2) 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: 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: Find length of QR

For points $Q(-1,5)$ and $R(-1,-4)$, $x_1=-1,y_1 = 5,x_2=-1,y_2=-4$.
$QR=\sqrt{(-1-(-1))^2+(-4 - 5)^2}=\sqrt{0+( - 9)^2}=9$.

Step3: Find length of RS

For points $R(-1,-4)$ and $S(5,2)$, $x_1=-1,y_1=-4,x_2 = 5,y_2=2$.
$RS=\sqrt{(5-(-1))^2+(2-(-4))^2}=\sqrt{(6)^2+(6)^2}=\sqrt{36 + 36}=\sqrt{72}=6\sqrt{2}\approx8.5$.

Step4: Find length of QS

For points $Q(-1,5)$ and $S(5,2)$, $x_1=-1,y_1 = 5,x_2=5,y_2=2$.
$QS=\sqrt{(5-(-1))^2+(2 - 5)^2}=\sqrt{(6)^2+(-3)^2}=\sqrt{36+9}=\sqrt{45}=3\sqrt{5}\approx6.7$.

Step5: Calculate perimeter

Perimeter $P=QR + RS+QS$.
$P=9 + 8.5+6.7 = 24.2$.

Answer:

$24.2$