daniko883y

2022-09-05

Find the slope of any line perpendicular to the line passing through (30,39) and (54,20)

Haylie Campbell

Beginner2022-09-06Added 13 answers

For the given points, we have

$\text{XXX}}\begin{array}{lll}\underline{x}& {\text{xxx}}& \underline{y}\\ 30& & 39\\ 54& & 20\\ {\text{XX}}& & {\text{XX}}\\ \underline{\Delta x}& & \underline{\Delta y}\\ -24& & 19\end{array$

By definition the slope of the line connecting these point is

$\text{XXX}}\frac{\Delta y}{\Delta x}=-\frac{19}{24$

Furthermore, if a line has a slope of m then any line perpendicular to it has a slope of $(-\frac{1}{{m}})$

Therefore any line perpendicular to the line through the given points

must have a slope of $(-\frac{1}{(-\frac{19}{24})})=\frac{24}{19}$

$\text{XXX}}\begin{array}{lll}\underline{x}& {\text{xxx}}& \underline{y}\\ 30& & 39\\ 54& & 20\\ {\text{XX}}& & {\text{XX}}\\ \underline{\Delta x}& & \underline{\Delta y}\\ -24& & 19\end{array$

By definition the slope of the line connecting these point is

$\text{XXX}}\frac{\Delta y}{\Delta x}=-\frac{19}{24$

Furthermore, if a line has a slope of m then any line perpendicular to it has a slope of $(-\frac{1}{{m}})$

Therefore any line perpendicular to the line through the given points

must have a slope of $(-\frac{1}{(-\frac{19}{24})})=\frac{24}{19}$

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