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 length of UV

Use distance formula for points $U(-2,4)$ and $V(3,4)$. Since $y$-coordinates are same, $UV=\vert3 - (-2)\vert$.
$UV=\vert3 + 2\vert=5$

Step2: Calculate length of VW

Use distance formula for points $V(3,4)$ and $W(3,-4)$. Since $x$-coordinates are same, $VW=\vert4-(-4)\vert$.
$VW=\vert4 + 4\vert = 8$

Step3: Calculate length of WU

Use distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ for points $W(3,-4)$ and $U(-2,4)$.
$WU=\sqrt{(-2 - 3)^2+(4+4)^2}=\sqrt{(-5)^2+8^2}=\sqrt{25 + 64}=\sqrt{89}\approx 9.43$

Step4: Calculate perimeter

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

Answer:

$22.43$