Question

The perpendicular from the origin to a line meets it at the point (-2, 9), find the equation of the line.

Answer 1

The slope of the line joining the origin (0, 0) and point (-2, 9) is $m_1=\frac{9-0}{-2-0}=\frac{-9}{2}$.
Accordingly, the slope of the line perpendicular to the line joining the origin and point (-2, 9) is
$m_2=\frac{-1}{m_1}=-\frac{1}{\left(-\frac{9}{2}\right)}=\frac{2}{9}$.
Now, the equation of the line passing through point (-2, 9) and having a slope $m_2$ is
$(y-9)=\frac{2}{9}(x+2)$
$9y-81=2x+4$
$i.e,2x-9y+85=0$