Chapter 5.2, Problem 15PSA

To determine

To Find: Whether $\overline{PQ}\parallel \overline{RS}$ , with explanation.

Answer to Problem 15PSA

  $\overline{PQ}\cancel{\parallel }\overline{RS}$ , since slope of lines $\overline{PQ}\text{and}\overline{RS}$ are not equal

Explanation of Solution

Given:

  $P=\left(-3,1\right),Q=\left(2,4\right),R=\left(1,-2\right)\text{ and }S=\left(7,2\right)$

Concept Used:

Two lines are parallel when their slopes are equal.

  $\text{Slope of line joining }\left(x_1,y_1\right)\text{and}\left(x_2,y_2\right)\text{is}m=\frac{y_2-y_1}{x_2-x_1}$

Calculation:

  $\begin{array}{l}\text{Slope of line joining }P=\left(-3,1\right)\text{and}Q=\left(2,4\right)\text{is}{m}_1=\frac{4-1}{2-\left(-3\right)}=\frac{3}{5}\left(1\right)\\ \text{Slope of line joining }R=\left(1,-2\right)\text{ and }S=\left(7,2\right)\text{is}{m}_2=\frac{2-\left(-2\right)}{7-1}=\frac{4}{6}=\frac{2}{3}\left(2\right)\\ \because m_1\ne m_2\\ \text{Since, we know that when two lines are parallel, their slope are also equal}\text{.}\\ \Rightarrow \overline{PQ}\cancel{\parallel }\overline{RS}\end{array}$