Question

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

Explanation:

Step1: Identify the coordinates

Given \( W(-5,-1) \) and \( X(2,6) \). Let \( (x_1,y_1)=(-5,-1) \) and \( (x_2,y_2)=(2,6) \).

Step2: Use the distance formula

The distance formula is \( d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \).
Substitute the values: \( x_2 - x_1=2-(-5)=2 + 5=7 \), \( y_2 - y_1=6-(-1)=6 + 1=7 \).
Then \( d=\sqrt{7^2+7^2}=\sqrt{49 + 49}=\sqrt{98}=\sqrt{49\times2}=7\sqrt{2} \).

Answer:

D. \( 7\sqrt{2} \)