Question

Please help Geometry problem

Answer 1

$\bf A(\stackrel{x_1}{-5}~,~\stackrel{y_1}{1})\qquad B(\stackrel{x_2}{-2}~,~\stackrel{y_2}{5}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{5-1}{-2-(-5)}\implies \cfrac{4}{-2+5}\implies \cfrac{4}{3} \\\\[-0.35em] ~\dotfill\\\\ B(\stackrel{x_2}{-2}~,~\stackrel{y_2}{5})\qquad C(\stackrel{x_2}{5}~,~\stackrel{y_2}{3})$

$\bf slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{3-5}{5-(-2)}\implies \cfrac{-2}{5+2}\implies -\cfrac{2}{7} \\\\[-0.35em] ~\dotfill \\\\ C(\stackrel{x_2}{5}~,~\stackrel{y_2}{3})\qquad D(\stackrel{x_2}{2}~,~\stackrel{y_2}{-1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies\cfrac{-1-3}{2-5}\implies \cfrac{-4}{-3}\implies \cfrac{4}{3} \\\\[-0.35em] ~\dotfill$

$\bf A(\stackrel{x_1}{-5}~,~\stackrel{y_1}{1})\qquad D(\stackrel{x_2}{2}~,~\stackrel{y_2}{-1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies\cfrac{-1-1}{2-(-5)}\implies \cfrac{-2}{2+5}\implies -\cfrac{2}{7}$