Question

trapezoid wxyz has vertices w(-1, 2), x(2, 2), y(3, -1), and z(-3, -1). is the trapezoid an isosceles trapezoid? select from the drop-down menu to correctly complete the statement. trapezoid wxyz choose... an isosceles trapezoid.

Explanation:

Step1: Identify parallel sides

First, check the slopes of all sides to find the two parallel bases of the trapezoid.
Slope of $WX$: $\frac{2-2}{2-(-1)} = \frac{0}{3} = 0$
Slope of $YZ$: $\frac{-1-(-1)}{-3-3} = \frac{0}{-6} = 0$
Slope of $XY$: $\frac{-1-2}{3-2} = \frac{-3}{1} = -3$
Slope of $ZW$: $\frac{2-(-1)}{-1-(-3)} = \frac{3}{2}$
Since slopes of $WX$ and $YZ$ are equal, $WX \parallel YZ$ (these are the two bases).

Step2: Calculate lengths of legs

For an isosceles trapezoid, the non-parallel sides (legs) must be equal in length. Use the distance formula $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$.
Length of $XY$: $\sqrt{(3-2)^2 + (-1-2)^2} = \sqrt{1^2 + (-3)^2} = \sqrt{1+9} = \sqrt{10}$
Length of $ZW$: $\sqrt{(-1-(-3))^2 + (2-(-1))^2} = \sqrt{2^2 + 3^2} = \sqrt{4+9} = \sqrt{13}$

Step3: Compare leg lengths

Since $\sqrt{10}
eq \sqrt{13}$, the legs are not congruent.

Answer:

is not