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

$\begin{array}{1 1}(A)\;m=2, c=\large\frac{5}{2} \\(B)\; m=-2, c=-\large\frac{5}{2} \\(C)\; m=-2, c=\large\frac{5}{2} \\(D)\;m=2, c=-\large\frac{5}{2} \end{array}$

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• If two lines are perpendicular then the product of their slope is -1.
Equation of the line is $y=mx+c$. The perpendicular from the origin meets the given line at (-1,2).
Hence the line joining the point (0,0) and (-1,2) is perpendicular to the given line.
$\therefore$ slope of the given line joining (0,0) and (-1,2) is $\large\frac{2-0}{-1-0}$$=-2 Slope of the given line is m. \therefore m \times -2=-1 \Rightarrow m = \large\frac{1}{2} The point (-1,2) lies on the given line. \therefore 2 = m(-1)+c \Rightarrow 2 = -\large\frac{1}{2}$$+c$