Question

Help please

Determine if the lines that pass through the given points are parallel, perpendicular or neither. Line A: (5, 10) and (12, 6) Line B: (-2, 4) and (5, 8)

Answer 1

`\bf slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{6-10}{12-5}\implies \stackrel{\textit{Line A}}{\boxed{\cfrac{-4}{7}}} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{-2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{8}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{8-4}{5-(-2)}\implies \cfrac{4}{5+2}\implies \stackrel{\textit{Line B}}{\boxed{\cfrac{4}{7}}}`

parallel lines have the same exact slope, well, this aren't equal, so they're not parallel.

perpendicular lines have negative reciprocal slopes, namely the slope of one, is the same as the other BUT negative and upside-down, well, the negative reciprocal of -4/7 is 7/4, so they're not perpendicular either. So neither then.