Question

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

Explanation:

Step1: Use the 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, \(x_1 = 2,y_1=-7,x_2 = 5,y_2=-4\).

Step2: Substitute the values into the formula

Substitute the values: \(d=\sqrt{(5 - 2)^2+(-4-(-7))^2}=\sqrt{(3)^2+(3)^2}\).

Step3: Simplify the expression

\(\sqrt{9 + 9}=\sqrt{18}=3\sqrt{2}\).

Answer:

E. \(3\sqrt{2}\)