Question

The perpendicular from the origin to the line $y=mx+c$ meets at the point $(-1,2)$. Then, the value of $m$ and $c$ respectively are

• A. $\frac{5}{2},\frac{1}{2}$
• B. $-\frac{5}{2},\frac{1}{2}$
• C. $-\frac{1}{2},\frac{5}{2}$
• D. $\frac{1}{2},\frac{5}{2}$

Answer 1

Answer: (D)

$\because$ Line $OP\perp$ Line $AB$
$\therefore$ Slope of $OP\times$ Slope of $AB=-1$
$\Rightarrow \frac{2-0}{-1-0}\times m=-1$
$\Rightarrow -2m=-1$
$\Rightarrow m=\frac{1}{2}$
Also, point $(-1,2)$ satisfies the line
$y=mx+c$
i.e., $2=\frac{1}{2}(-1)+c$ (putting $x=-1,y=2)$

$\Rightarrow 2=-\frac{1}{2}+c$
$\Rightarrow c=2+\frac{1}{2}=\frac{5}{2}$
Hence, $m=\frac{1}{2},c=\frac{5}{2}$