Points (2, 0) and (0, 3) lie on line k. What is the slope of the line that is perpendicular to k

Answered by admin AT 16/04/2020 - 06:03 PM

$\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 2}}\quad ,&{{ 0}})\quad 
% (c,d)
&({{ 0}}\quad ,&{{ 3}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{3-0}{0-2}\implies \boxed{\cfrac{-3}{2}}\\\\
-------------------------------\\\\$

$\bf \textit{perpendicular lines have, negative-reciprocal slope}\\\\
slope=\cfrac{a}{{{ b}}}\qquad negative\implies -\cfrac{a}{{{ b}}}\qquad reciprocal\implies - \cfrac{{{ b}}}{a}\\\\
-------------------------------\\\\
thus
\\\\\\
\cfrac{-3}{2}\qquad negative\implies \cfrac{3}{2}\qquad reciprocal\implies \boxed{\cfrac{2}{3}}$

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Points (2, 0) and (0, 3) lie on line k. What is the slope of the line that is perpendicular to k

Answered by admin AT 16/04/2020 - 06:03 PM

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