Question

determine the most precise name for quadrilateral wxyz.
o rectangle
o quadrilateral
o parallelogram
o rhombus

Explanation:

Step1: Calculate the slopes of the sides

The slope formula is \(m = \frac{y_2 - y_1}{x_2 - x_1}\).
For \(WZ\): \(W(3,4)\), \(Z(0,3)\), \(m_{WZ}=\frac{3 - 4}{0 - 3}=\frac{-1}{-3}=\frac{1}{3}\).
For \(XY\): \(X(4,-1)\), \(Y(0,-3)\), \(m_{XY}=\frac{-3+1}{0 - 4}=\frac{-2}{-4}=\frac{1}{2}\).
For \(WX\): \(W(3,4)\), \(X(4,-1)\), \(m_{WX}=\frac{-1 - 4}{4 - 3}=\frac{-5}{1}=-5\).
For \(ZY\): \(Z(0,3)\), \(Y(0,-3)\), \(m_{ZY}=\frac{-3 - 3}{0 - 0}\), undefined (vertical line).

Step2: Check for parallel sides

In a parallelogram, opposite sides are parallel (equal slopes).
Since \(m_{WZ}
eq m_{XY}\) and \(m_{WX}
eq m_{ZY}\), it's not a parallelogram.
A rectangle is a type of parallelogram (so ruled out).
A rhombus is a parallelogram with all sides equal (also ruled out as not a parallelogram).
A quadrilateral is a four - sided figure, which \(WXYZ\) is.

Answer:

quadrilateral