Chapter 6.4, Problem 48HP

To determine

The equations of four lines having intersections that forms the vertices of a rectangle.

Answer to Problem 48HP

  $x=0,x=3,y=0,y=2.$

Explanation of Solution

A parallelogram with 4 right angles is a rectangle. Both pairs of opposite sides of a rectangle are congruent and parallel.

Thus, the horizontal and vertical lines of a rectangle are parallel and form right angles.

Let the sides of the rectangle be;

  $\begin{array}{l}x=0\text{ and y = 0}\\ \text{and;}\\ x=3\text{ and y = 2}\end{array}$

The intersection points will be;

The lines of rectangle are:

  $x=0,x=3,y=0,y=2.$

The vertices will be:

  $A\left(0,2\right),B\left(0,0\right),C\left(3,2\right),D\left(3,0\right).$