Question

what is the perimeter of rectangle jklm, with vertices j(-1, 3), k(2, 3), l(2, -5), and m(-1, -5)?
22 units
10 units
6 units
18 units

Explanation:

Step1: Calculate length of side JK

Use distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For points $J(-1,3)$ and $K(2,3)$, $x_1=-1,y_1 = 3,x_2=2,y_2 = 3$. Then $JK=\sqrt{(2-(-1))^2+(3 - 3)^2}=\sqrt{3^2+0^2}=3$.

Step2: Calculate length of side KL

For points $K(2,3)$ and $L(2,-5)$, $x_1 = 2,y_1=3,x_2=2,y_2=-5$. Then $KL=\sqrt{(2 - 2)^2+(-5 - 3)^2}=\sqrt{0^2+(-8)^2}=8$.

Step3: Calculate perimeter of rectangle

In a rectangle, opposite sides are equal. Perimeter $P=2(JK + KL)$. Substitute $JK = 3$ and $KL=8$ into the formula: $P=2(3 + 8)=2\times11 = 22$.

Answer:

22 units