Question

post test: coordinate geometry
what is the length of \overline{wx}?
a. 6
b. 12
c. 16
d. 2\sqrt{3}
e. 6\sqrt{2}

Explanation:

Step1: Find the coordinates of points

From the graph, the coordinates of \(X\) are \((-1,-9)\) and of \(W\) are \((5,-3)\).

Step2: 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 \(x_1=-1,y_1 = -9,x_2 = 5,y_2=-3\).
Substitute into the formula: \(d=\sqrt{(5-(-1))^2+(-3-(-9))^2}=\sqrt{(5 + 1)^2+(-3 + 9)^2}\).

Step3: Simplify the expression

First, calculate \((5 + 1)^2=36\) and \((-3 + 9)^2=36\). Then \(d=\sqrt{36+36}=\sqrt{72}\).
Factor \(72\) as \(36\times2\), so \(d=\sqrt{36\times2}=6\sqrt{2}\).

Answer:

E. \(6\sqrt{2}\)