Question

the points t(-6,2), u(2,2), and v(-3,9) 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.
answer attempt 1 out of 2
perimeter = 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 T(-6,2) and U(2,2)

$d_{TU}=\sqrt{(2-(-6))^2+(2 - 2)^2}=\sqrt{(2 + 6)^2+0^2}=\sqrt{8^2}=8$.

Step3: Calculate distance between U(2,2) and V(-3,9)

$d_{UV}=\sqrt{(-3 - 2)^2+(9 - 2)^2}=\sqrt{(-5)^2+7^2}=\sqrt{25 + 49}=\sqrt{74}\approx8.6$.

Step4: Calculate distance between V(-3,9) and T(-6,2)

$d_{VT}=\sqrt{(-6-(-3))^2+(2 - 9)^2}=\sqrt{(-6 + 3)^2+(-7)^2}=\sqrt{(-3)^2+(-7)^2}=\sqrt{9 + 49}=\sqrt{58}\approx7.6$.

Step5: Calculate perimeter

$P=d_{TU}+d_{UV}+d_{VT}=8 + 8.6+7.6 = 24.2$.

Answer:

$24.2$