Question

select the correct answer.
the endpoints of \\(\overline{wx}\\) are \\(w(2,-7)\\) and \\(x(5,-4)\\).
what is the length of \\(\overline{wx}\\)?
a. \\( 3 \\)
b. \\( 6 \\)
c. \\( 18 \\)
d. \\( \sqrt{6} \\)
e. \\( 3\sqrt{2} \\)

Explanation:

Step1: Recall distance formula

For points $(x_1,y_1)$ and $(x_2,y_2)$, length $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Step2: Substitute given coordinates

Let $(x_1,y_1)=(2,-7)$, $(x_2,y_2)=(5,-4)$.
$$d=\sqrt{(5-2)^2+(-4-(-7))^2}$$

Step3: Simplify inside the square root

$$d=\sqrt{(3)^2+(3)^2}=\sqrt{9+9}$$

Step4: Calculate final value

$$d=\sqrt{18}=3\sqrt{2}$$

Answer:

E. $3\sqrt{2}$