Question

10 multiple choice 1 point julie wants to show that a quadrilateral with vertices j(2, 3), k(2,7), l(-2,7), m(-2,3) is a square. using the distance formula, what should she find the length of each side to be? 2 8 3 4

Explanation:

Step1: Recall distance formula

The distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.

Step2: Calculate side JK

Take $J(2,3)$ and $K(2,7)$:
$d_{JK}=\sqrt{(2-2)^2+(7-3)^2}=\sqrt{0+16}=4$

Step3: Verify adjacent side KL

Take $K(2,7)$ and $L(-2,7)$:
$d_{KL}=\sqrt{(-2-2)^2+(7-7)^2}=\sqrt{16+0}=4$

Step4: Confirm consistency (optional)

Take $L(-2,7)$ and $M(-2,3)$:
$d_{LM}=\sqrt{(-2+2)^2+(3-7)^2}=\sqrt{0+16}=4$
Take $M(-2,3)$ and $J(2,3)$:
$d_{MJ}=\sqrt{(2+2)^2+(3-3)^2}=\sqrt{16+0}=4$

Answer:

4