Question

what is the length of \overline{wx}?
a. 3
b. 6
c. 18
d. \sqrt{6}
e. 3\sqrt{2}

Explanation:

Step1: Find coordinates of \(W\) and \(X\)

From the graph, \(W=(0, - 7)\) and \(X=(3, - 4)\).

Step2: Use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

Here \(x_1 = 0,y_1=-7,x_2 = 3,y_2=-4\).
Substitute into the formula: \(d=\sqrt{(3 - 0)^2+(-4+7)^2}\).

Step3: Simplify the expression

First, calculate \((3 - 0)^2=9\) and \((-4 + 7)^2=9\).
Then \(d=\sqrt{9 + 9}=\sqrt{18}\).
Simplify \(\sqrt{18}=\sqrt{9\times2}=3\sqrt{2}\).

Answer:

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