Question

Given P(-3, 9), Q(8,-2), R(-8, 8), and S(0, y). Find y such that PQ || RS.
Answer: y

Answer 1

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the PQ line

`P(\stackrel{x_1}{-3}~,~\stackrel{y_1}{9})\qquad Q(\stackrel{x_2}{8}~,~\stackrel{y_2}{-2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{9}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{(-3)}}} \implies \cfrac{-11}{8 +3}\implies -1`

if indeed RS || PQ, then their slopes are exactly the same, thus

`R(\stackrel{x_1}{-8}~,~\stackrel{y_1}{8})\qquad S(\stackrel{x_2}{0}~,~\stackrel{y_2}{y}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{y}-\stackrel{y1}{8}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{(-8)}}} \implies \cfrac{y -8}{0 +8}~~ = ~~\stackrel{\stackrel{slope}{\downarrow }}{-1} \\\\\\ \cfrac{y-8}{8}=-1\implies y-8=-8\implies \boxed{y=0}`