Question

A line segment has endpoints A(3,-2) and B(-7,10). What is the slope of a line perpendicular to AB?

Answer 1

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of AB firstly

`A(\stackrel{x_1}{3}~,~\stackrel{y_1}{-2})\qquad B(\stackrel{x_2}{-7}~,~\stackrel{y_2}{10}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{10}-\stackrel{y1}{(-2)}}}{\underset{\textit{\large run}} {\underset{x_2}{-7}-\underset{x_1}{3}}} \implies \cfrac{ 10 +2 }{ -10 } \implies \cfrac{ 12 }{ -10 } \implies -\cfrac{6}{5} \\\\[-0.35em] ~\dotfill`

`\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{-6}{5}} ~\hfill \stackrel{reciprocal}{\cfrac{5}{-6}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{5}{-6} \implies \cfrac{5}{ 6 }}}`