The perpendicular from the origin to the line y = mx + c meets it at the point


The perpendicular from the origin to the line y = mx + c meets it at the point

(1, 2). Find the values of and c.


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.

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

The slope of the given line is m.

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

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

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

$\therefore 2=m(-1)+c$

$\Rightarrow 2=\frac{1}{2}(-1)+c$

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

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

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