Question

z(0, 3) h(3, 4) x(4, -1) y(0, -3) rectangle trapezoid parallelogram quadrilateral

Explanation:

Step1: Recall the properties of quadrilaterals

A quadrilateral is a four - sided polygon. A rectangle has four right angles, a trapezoid has one pair of parallel sides, and a parallelogram has two pairs of parallel sides.

Step2: Analyze the given figure

The figure has four sides, so it is a quadrilateral. To check if it is a rectangle, we can find the slopes of the sides. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$.
The slope of $YZ$ with $Y(0,-3)$ and $Z(0,3)$ is undefined ($x_1 = x_2=0$). The slope of $ZW$ with $Z(0,3)$ and $W(3,4)$ is $m_{ZW}=\frac{4 - 3}{3 - 0}=\frac{1}{3}$. The slope of $WX$ with $W(3,4)$ and $X(4,-1)$ is $m_{WX}=\frac{-1 - 4}{4 - 3}=-5$. The slope of $XY$ with $X(4,-1)$ and $Y(0,-3)$ is $m_{XY}=\frac{-3+1}{0 - 4}=\frac{1}{2}$. Since the product of the slopes of adjacent sides is not - 1 (no right - angles), it is not a rectangle. Also, it does not have one pair of parallel sides (so not a trapezoid) and does not have two pairs of parallel sides (so not a parallelogram).

Answer:

quadrilateral