Chapter 6.2, Problem 22PPS

To determine

The coordinates of the intersection of the diagonals of figure with given vertices.

Answer to Problem 22PPS

The coordinates of the intersection of diagonals are (0, 1.5).

Explanation of Solution

Given:

The given vertices are:

  $W\left(-4,5\right),X\left(5,7\right),Y\left(4,-2\right),Z\left(-5,-4\right).$

Calculation:

The diagonals of a parallelogram bisect each other.

As the diagonals of parallelogram bisect each other, their intersection point is the midpoint of line segments WY and XZ.

So, the mid-point of line WY with W (-4, 5) and Y (4, -2):

  $\begin{array}{l}M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\\ M=\left(\frac{-4+4}{2},\frac{5-2}{2}\right)\\ M=\left(0,1.5\right)\end{array}$

The coordinates of the intersection of diagonals are (0, 1.5).

Now, the mid-point of line XZ with X (5, 7) and Z (-5, -4):

  $\begin{array}{l}M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\\ M=\left(\frac{5-5}{2},\frac{7-4}{2}\right)\\ M=\left(0,1.5\right)\end{array}$

The coordinates of the intersection of diagonals are (0, 1.5).