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 the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ to find the length of $UV$.

For points $U(-2,4)$ and $V(3,4)$, $x_1=-2,y_1 = 4,x_2=3,y_2 = 4$.
$UV=\sqrt{(3 - (-2))^2+(4 - 4)^2}=\sqrt{(3 + 2)^2+0^2}=\sqrt{25}=5$

Step2: Use the distance formula to find the length of $VW$.

For points $V(3,4)$ and $W(3,-4)$, $x_1 = 3,y_1=4,x_2 = 3,y_2=-4$.
$VW=\sqrt{(3 - 3)^2+(-4 - 4)^2}=\sqrt{0+( - 8)^2}=\sqrt{64}=8$

Step3: Use the distance formula to find the length of $WU$.

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

Step4: Calculate the perimeter $P$.

$P=UV + VW+WU=5 + 8+9.43=22.43$

Answer:

$22.43$