Question

The perpendicular from the origin to the line y = mx + c meets it at the point (-1, 2).

Find the value of m and c.

Answer 1

Equation of the line PQ

$y-0=\left(\frac{2-0}{-1-0}\right)(x-0)$

$\Rightarrow y=-2x\Rightarrow 2x+y=0$ . . . (i)

Slope of the required line which is perpendicular to line(i) is $\frac{1}{2}$

$\therefore$ Equation of the line AB is

$y-2=\frac{1}{2}(x+1)$

$\Rightarrow 2y-4=x+1$

$\Rightarrow 2y=x+5\Rightarrow y=\frac{x}{2}+\frac{5}{2}$

Comparing it with y = mx + c, we have

$m=\frac{1}{2}$ and $c=\frac{5}{2}$.