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: Calculate distance between U and V

Use distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For $U(-2,4)$ and $V(3,4)$, $x_1=-2,y_1 = 4,x_2=3,y_2 = 4$. Then $d_{UV}=\sqrt{(3 - (-2))^2+(4 - 4)^2}=\sqrt{(5)^2+0^2}=5$.

Step2: Calculate distance between V and W

For $V(3,4)$ and $W(3,-4)$, $x_1 = 3,y_1=4,x_2 = 3,y_2=-4$. Then $d_{VW}=\sqrt{(3 - 3)^2+(-4 - 4)^2}=\sqrt{0+( - 8)^2}=8$.

Step3: Calculate distance between W and U

For $W(3,-4)$ and $U(-2,4)$, $x_1 = 3,y_1=-4,x_2=-2,y_2 = 4$. Then $d_{WU}=\sqrt{(-2 - 3)^2+(4-( - 4))^2}=\sqrt{(-5)^2+(8)^2}=\sqrt{25 + 64}=\sqrt{89}\approx9.43$.

Step4: Calculate perimeter

Perimeter $P=d_{UV}+d_{VW}+d_{WU}=5 + 8+9.43=22.43$.

Answer:

$22.43$