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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$
$\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.
answered May 13, 2014 by thanvigandhi_1

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