Question

select the correct answer. the endpoints of $overline{wx}$ are $w(-5,-1)$ and $x(2,6)$. what is the length of $overline{wx}$? a. 7 b. 14 c. $4sqrt{2}$ d. $7sqrt{2}$

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $(x_1,y_1)=(-5,-1)$ and $(x_2,y_2)=(2,6)$.

Step2: Calculate differences

$x_2 - x_1=2-(-5)=7$ and $y_2 - y_1=6 - (-1)=7$.

Step3: Substitute into formula

$d=\sqrt{(7)^2+(7)^2}=\sqrt{49 + 49}=\sqrt{98}$.

Step4: Simplify the square - root

$\sqrt{98}=\sqrt{49\times2}=7\sqrt{2}$.

Answer:

D. $7\sqrt{2}$