# Question #dccca

Jan 22, 2018

See a solution process below:

#### Explanation:

The slope of a line can be found by using the formula: $m = \frac{\textcolor{red}{{y}_{2}} - \textcolor{b l u e}{{y}_{1}}}{\textcolor{red}{{x}_{2}} - \textcolor{b l u e}{{x}_{1}}}$

Where $m$ is the slope and ($\textcolor{b l u e}{{x}_{1} , {y}_{1}}$) and ($\textcolor{red}{{x}_{2} , {y}_{2}}$) are the two points on the line.

The slope of the line passing through $\left(- 3 , 4\right)$ and $\left(1 , 2\right)$ is:

${m}_{1} = \frac{\textcolor{red}{2} - \textcolor{b l u e}{4}}{\textcolor{red}{1} - \textcolor{b l u e}{- 3}} = \frac{\textcolor{red}{2} - \textcolor{b l u e}{4}}{\textcolor{red}{1} + \textcolor{b l u e}{3}} = - \frac{2}{4} = - \frac{1}{2}$

The slope of the line passing through $\left(- 1 , 3\right)$ and $\left(1 , 1\right)$ is:

${m}_{2} = \frac{\textcolor{red}{1} - \textcolor{b l u e}{3}}{\textcolor{red}{1} - \textcolor{b l u e}{- 1}} = \frac{\textcolor{red}{1} - \textcolor{b l u e}{3}}{\textcolor{red}{1} + \textcolor{b l u e}{1}} = - \frac{2}{2} = - 1$

Given a line with slope $m$, a line perpendicular to this line, let's call it ${m}_{p}$ will have a slope the negative inverse of the original line. Or:

${m}_{p} = - \frac{1}{m}$

The line perpendicular to the first line therefore would have a slope:

${m}_{p 1} = \frac{- 1}{- \frac{1}{2}} = 2$

This is not the slope of the second line therefore these two lines are not perpendicular.

Jan 22, 2018

Using slope

#### Explanation:

Slope $m = \frac{y 2 - y 1}{x 2 - x 1}$
And for 2 lines to be perpendicular the product of their slopes must be = -1
Therefore on finding the slopes we get
$m 1 = \frac{2 - 4}{1 - \left(- 3\right)} = - \frac{1}{2}$
$m 2 = \frac{1 - 3}{1 - \left(- 1\right)} = - \frac{2}{2} = - 1$
But $m 1 \cdot m 2 \ne - 1$
Hence they are not perpendicular
Hope u find it helpful :)