Question

The perpendicular 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 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.

$∴ m\times-2=-1$ [The two lines are perpendicular]

$⇒m=\frac{1}{2}$
Since point $(-1, 2)$ lies on the given line, it satisfies the equation $y = mx + c.$
$∴ 2=m(-1)+c$

$⇒ 2=\frac{1}{2}(-1)+c$

$⇒ c = 2+\frac{1}{2} =\frac{ 5}{2}$

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