Question

on the coordinate plane, rectangle jklm has vertices j(-2, 2), k(6, -4), l(3, -8), and m(-5, -2). what is the perimeter of rectangle jklm? if necessary, round your answer to the nearest tenth. units

Explanation:

Step1: Calculate the length of side JK

Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For points $J(-2,2)$ and $K(6,-4)$, $x_1=-2,y_1 = 2,x_2=6,y_2=-4$. Then $JK=\sqrt{(6 - (-2))^2+((-4)-2)^2}=\sqrt{8^2+(-6)^2}=\sqrt{64 + 36}=\sqrt{100}=10$.

Step2: Calculate the length of side KL

For points $K(6,-4)$ and $L(3,-8)$, $x_1 = 6,y_1=-4,x_2=3,y_2=-8$. Then $KL=\sqrt{(3 - 6)^2+((-8)-(-4))^2}=\sqrt{(-3)^2+(-4)^2}=\sqrt{9 + 16}=\sqrt{25}=5$.

Step3: Calculate the perimeter of the rectangle

The opposite - sides of a rectangle are equal, so the perimeter $P=2(JK + KL)$. Substitute $JK = 10$ and $KL = 5$ into the formula, $P=2(10 + 5)=30$.

Answer:

30