Chapter 6.3, Problem 26PPS

To determine

The graph of each quadrilateral with given vertices and whether the figure forms a parallelogram or not.

Answer to Problem 26PPS

VWXY is not a parallelogram.

Explanation of Solution

Given:

The given vertices are:

  $V\left(3,5\right),W\left(1,-2\right),X\left(-6,2\right),Y\left(-4,7\right).$

Calculation:

Parallelogram has both pairs of its opposite sides as parallel sides.

The quadrilateral with given vertices will be:

The slope of line segment YV will be:

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

The slope of line segment WX will be:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{2-\left(-2\right)}{-6-1}\\ m=\frac{4}{-7}\\ m=-\frac{4}{7}\end{array}$

The slope of line segment YX will be:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{2-7}{-6-\left(-4\right)}\\ m=\frac{-5}{-2}\\ m=\frac{5}{2}\end{array}$

The slope of line segment VW will be:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{-2-5}{1-3}\\ m=\frac{-7}{-2}\\ m=\frac{7}{2}\end{array}$

The slope of line YV is not equal to the slope of line WX and the slope of line YX is not equal to the slope of VW.

Therefore, by the definition of a parallelogram, VWXY is not a parallelogram.