Chapter 6.3, Problem 50SPR

To determine

The coordinates of the intersection of diagonals of parallelogram ABCD.

Answer to Problem 50SPR

The coordinates of the intersection of diagonals are $\left(1,0.5\right)$ .

Explanation of Solution

Given:

The vertices of the parallelogram are:

  $A\left(-3,5\right),B\left(6,5\right),C\left(5,-4\right),D\left(-4,-4\right)$

Calculation:

The diagonals of a parallelogram bisect each other and both diagonals have the same midpoint. Therefore, the intersection point is the midpoint of line AC and BD.

The midpoint of AC will be:

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

The coordinates of the intersection of diagonals are $\left(1,0.5\right)$ .