Chapter 6.2, Problem 6CYU

To determine

The coordinates of the intersection of diagonals in given parallelogram.

Answer to Problem 6CYU

The coordinates of the intersection of the diagonals are (0,2).

Explanation of Solution

Given:

The given vertices are:

  $A\left(-4,6\right),B\left(5,6\right),C\left(4,-2\right),D\left(-5,-2\right).$

Calculation:

The diagonals in a parallelogram bisect each other.

As the diagonals bisect each other, the intersection point will be the mid-point of AC and BD.

Therefore, the mid-point of AC will be:

  $\begin{array}{l}M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\\ M=\left(\frac{-4+4}{2},\frac{6-2}{2}\right)\\ M=\left(0,2\right)\end{array}$

Therefore, the coordinates of the intersection of the diagonals are (0,2).