Question

The perpendicualar from the origin to the line $y=mx+c$ meets it at the point (-1,2). Find the values of m and c.

Answer 1

The given equation of the line is $y=mx+c$

It is given that the perpendicular from the origin meets the given line at (-1,2).

Therefore, the line joining the points (0,0) and (-1,2) is perpendicular to the given line.

Slope of the line joining (0,0) and (-1,2) = $\frac{2}{-1}=2$

The slope of the given line is m.

$m\times -2=-1$

$m=\frac{1}{2}$

Since point (-1,2) lies on the given line, it satisfies the equation $y=mx+c$.

Therefore,

$2=m(-1)+c$

$c=2+\frac{1}{2}=\frac{5}{2}$

Thus, the respective values of m and c are $\frac{1}{2}$ and $\frac{5}{2}$.