Question

find the perimeter of the polygon with the vertices u(-2,4), v(3,4), and w(3, - 4). round your answer to the nearest hundredth. the perimeter is about □ units.

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: Calculate distance between U(-2,4) and V(3,4)

$d_{UV}=\sqrt{(3 - (-2))^2+(4 - 4)^2}=\sqrt{(3 + 2)^2+0^2}=\sqrt{25}=5$

Step3: Calculate distance between V(3,4) and W(3,-4)

$d_{VW}=\sqrt{(3 - 3)^2+(-4 - 4)^2}=\sqrt{0+(-8)^2}=\sqrt{64}=8$

Step4: Calculate distance between W(3,-4) and U(-2,4)

$d_{WU}=\sqrt{(-2 - 3)^2+(4-(-4))^2}=\sqrt{(-5)^2+(4 + 4)^2}=\sqrt{25 + 64}=\sqrt{89}\approx 9.43$

Step5: Calculate perimeter

$P=d_{UV}+d_{VW}+d_{WU}=5 + 8+9.43 = 22.43\approx22.43$

Answer:

$22.43$