$\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$

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

Hence the values of $m$ and $c$ are -2 and $ \large\frac{5}{2}$ respectively.

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