Question

Given W (9,8), X (8, 3), Y (2, 5), and Z(x, 0). Find x such that WX || YZ.

Answer 1

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

`W(\stackrel{x_1}{9}~,~\stackrel{y_1}{8})\qquad X(\stackrel{x_2}{8}~,~\stackrel{y_2}{3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{8}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{9}}} \implies \cfrac{-5}{-1}\implies 5`

well, hell, that means that YZ has a slope of 5 as well, so then

`Y(\stackrel{x_1}{2}~,~\stackrel{y_1}{5})\qquad Z(\stackrel{x_2}{x}~,~\stackrel{y_2}{0}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{0}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{x}-\underset{x_1}{2}}} ~~ = ~~ \stackrel{\stackrel{m}{\downarrow }}{5}\implies \cfrac{-5}{x-2}=5\implies -5=5x-10 \\\\\\ 5=5x\implies \cfrac{5}{5}=x\implies {\Large \begin{array}{llll} 1=x \end{array}}`