Chapter 4.3, Problem 42PPS

To determine

Whether the points are vertices of a rectangle.

Answer to Problem 42PPS

The given two lines are not parallel.

Explanation of Solution

Given information:

A must enter the coordinates for points on the design. One line segment she drew has endpoints of $\left(-2,1\right)$ and $\left(4,3\right)$ . The other coordinates that A entered are $\left(2,-7\right)$ and $\left(8,-3\right)$ .

Calculation:

The slope of the line $m_1$ joining the points $R\left(-2,1\right)$ and $S\left(4,3\right)$

  $\begin{array}{c}{m}_1=\frac{3-1}{4-\left(-2\right)}\\ =\frac{2}{6}\\ =\frac{1}{3}\end{array}$

The slope of the line $m_2$ joining the points $J\left(2,-7\right)$ and $k\left(8,-3\right)$

  $\begin{array}{c}{m}_2=\frac{-3-\left(-7\right)}{8-2}\\ =\frac{4}{6}\\ =\frac{2}{3}\end{array}$

Here $m_1$ is not equal to $m_2$ .

Therefore, the given two lines are not parallel.