Chapter 5.3, Problem 18PSB

To determine

To Find: Why the lines m and n are parallel, with the explanation.

Answer to Problem 18PSB

  $\overleftrightarrow{m}\parallel \overleftrightarrow{n}$ , since slope of lines $\overleftrightarrow{m}\text{and}\overleftrightarrow{n}$ are equal

Explanation of Solution

Given:

  

  $A=\left(1,5\right),B=\left(4,9\right),C=\left(6,0\right)\text{ and }D=\left(9,4\right)$

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:

  $\begin{array}{l}\text{Slope of line joining }A=\left(1,5\right)\text{and }B=\left(4,9\right)\text{is}{m}_1=\frac{9-5}{4-1}=\frac{4}{3}\left(1\right)\\ \text{Slope of line joining }C=\left(6,0\right)\text{ and }D=\left(9,4\right)\text{is}{m}_2=\frac{4-0}{9-6}=\frac{4}{3}\left(2\right)\\ \because m_1=m_2\\ \text{Since, we know that when two lines are parallel, their slope are also equal}\text{.}\\ \Rightarrow \overline{AB}\parallel \overline{CD}\\ \Rightarrow \overleftrightarrow{m}\parallel \overleftrightarrow{n}\end{array}$