Question

the endpoints of $overline{wx}$ are $w(5, -3)$ and $x(-1, -9)$. what is the length of $overline{wx}$? a. 6 b. 12 c. 16 d. $2\sqrt{3}$ e. $6\sqrt{2}$

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: Assign coordinates

Let $(x_1,y_1)=(5,-3)$ and $(x_2,y_2)=(-1,-9)$

Step3: Calculate differences

$\Delta x = -1-5=-6$, $\Delta y = -9-(-3)=-6$

Step4: Substitute into formula

$d=\sqrt{(-6)^2+(-6)^2}=\sqrt{36+36}=\sqrt{72}$

Step5: Simplify the radical

$\sqrt{72}=\sqrt{36\times2}=6\sqrt{2}$

Answer:

E. $6\sqrt{2}$