The perpendicular from the origin to the line y = mx + c meets it… - Vidyadip

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.

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Answer

OP is perpendicular to the given line y = mx + c $\therefore$ (Slope of OP) × (Slope of line) = -1 $\frac{2-0}{-1-0}\times\text{m}=-1$ $\text{m}=\frac{-1\times-1}{2}=\frac{1}{2}$ and (-1, 2) lies on the line $\text{y}=\frac{1}{2}+\text{c}$ $\therefore2=\frac{1}{2}(-1)+\text{c}$ $\text{c}=2+\frac{1}{2}=\frac{5}{2}$ $\therefore\text{c}=\frac{5}{2}$ and $\text{m}=\frac{1}{2}$

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