Chapter 6.6, Problem 61PPS

To determine

Whether each figure is trapezoid, a parallelogram, a square, a rhombus or a quadrilateral.

Answer to Problem 61PPS

WXYZ is not a parallelogram.

Explanation of Solution

Given:

The given vertices are:

  $\text{W}\left(-3,4\right)\text{,X}\left(3,4\right)\text{,Y}\left(5,3\right)\text{,Z}\left(-5,1\right)\text{.}$

Calculation:

Draw the quadrilateral from given vertices;

  

Consider the diagonals of the figure.

If a quadrilateral is a parallelogram, the diagonals bisect each other.

Finding the midpoint of WZ:

  $\begin{array}{l}M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\\ M=\left(\frac{-3+5}{2},\frac{4+3}{2}\right)\\ M=\left(1,\frac{7}{2}\right)\end{array}$

Finding the midpoint of XY;

  $\begin{array}{l}M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\\ M=\left(\frac{3+5}{2},\frac{4+3}{2}\right)\\ M=\left(4,\frac{7}{2}\right)\end{array}$

As the midpoints are not equal, the diagonals do not bisect each other.

Hence, WXYZ is not a parallelogram.