Question

X

A line passes through points at (9, 5) and (4, 3). What is the slope of the line perpendicular to this line? Slope

Answer 1

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

`(\stackrel{x_1}{9}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{3}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{3}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{9}}} \implies \cfrac{ -2 }{ -5 } \implies \cfrac{2}{5} \\\\[-0.35em] ~\dotfill`

`\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{2}{5}} ~\hfill \stackrel{reciprocal}{\cfrac{5}{2}} ~\hfill \stackrel{negative~reciprocal}{\boxed{-\cfrac{5}{2}} }}`