Chapter 6.3, Problem 7CYU

To determine

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

Answer to Problem 7CYU

WXYZ is a parallelogram.

Explanation of Solution

Given:

The given vertices are:

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

Calculation:

The quadrilateral with given vertices will be:

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

Calculating the midpoint of line segment WY.

  $\begin{array}{l}M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\\ M=\left(\frac{-5+1}{2},\frac{4-3}{2}\right)\\ M=\left(-2,0.5\right)\end{array}$

Calculating the midpoint of line segment XZ.

  $\begin{array}{l}M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\\ M=\left(\frac{3-7}{2},\frac{4-3}{2}\right)\\ M=\left(-2,0.5\right)\end{array}$

The midpoint of WY and XZ is (-2, 0.5), which means that the diagonals bisect each other.

Therefore, by the definition of a parallelogram, WXYZ is a parallelogram.