daniko883y

2022-09-05

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

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Haylie Campbell

Expert

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 $\left(-\frac{1}{m}\right)$

Therefore any line perpendicular to the line through the given points
must have a slope of $\left(-\frac{1}{\left(-\frac{19}{24}\right)}\right)=\frac{24}{19}$

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