Question

I need helpppp please

Answer 1

to get the slope of any straight line, we simply need two points off of it, let's use those in the picture below.

`\stackrel{\textit{\LARGE line of reflection}}{(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-2})} \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-1)}}} \implies \cfrac{-2 +4}{1 +1} \implies \cfrac{ 2 }{ 2 } \implies \text{\LARGE 1}`

now, keeping in mind that perpendicular lines have negative reciprocal slopes, there are three dotted lines, each one of them, hits the line of reflection perpendicularly, so their slope must be

`\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{1\implies \cfrac{\boxed{1}}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{\boxed{1}}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{\boxed{1}}\implies \text{\LARGE -1}}}`