Question

Use slope to determine if lines AB and CD are parallel, perpendicular or neither. A(2, 3) B(-1, 4) C(-5, 3) D(-4, 6)

Answer 1

`A(\stackrel{x_1}{2}~,~\stackrel{y_1}{3})\qquad B(\stackrel{x_2}{-1}~,~\stackrel{y_2}{4}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{3}}}{\underset{\textit{\large run}} {\underset{x_2}{-1}-\underset{x_1}{2}}} \implies \cfrac{ 1 }{ -3 } \implies -\cfrac{1}{3} \\\\[-0.35em] ~\dotfill`

`C(\stackrel{x_1}{-5}~,~\stackrel{y_1}{3})\qquad D(\stackrel{x_2}{-4}~,~\stackrel{y_2}{6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{6}-\stackrel{y1}{3}}}{\underset{\textit{\large run}} {\underset{x_2}{-4}-\underset{x_1}{(-5)}}} \implies \cfrac{ 3 }{-4 +5} \implies \cfrac{ 3 }{ 1 } \implies 3\qquad \textit{\LARGE perpendicular}`

keeping in mind that perpendicular lines have negative reciprocal slopes, let's notice, AB has a slope that is the same as CD's but negative and upside-down.