Question

Find the slope of the line perpendicular to the line joining the points $(2,-3)$ and $(1,4)$.

Answer 1

We know that the slope of the line joining two points $(x_1,y_1)$ and $(x_2,y_2)$ is:

$m=\frac{y_2-y_1}{x_2-x_1}$

Here, the given points are $(2,-3)$ and $(1,4)$, therefore, the slope of the line is:

$m_1=\frac{y_2-y_1}{x_2-x_1}=\frac{4-(-3)}{1-2}=\frac{7}{-1}=-7$

We also know that if the slope of the two lines have the relation $m_1\times m_2=-1$, then the lines are perpendicular to each other, therefore, the slope $m_2$ of the line perpendicular to the given line is:

$m_1\times m_2=-1\Rightarrow -7\times m_2=-1\Rightarrow -7m_2=-1\Rightarrow m_2=\frac{1}{7}$

Hence, the slope of the line perpendicular to the given line is$\frac{1}{7}$.