The given equation of line is \(y = mx + c.\)
It is given that the perpendicular from the origin meets the given line at \((-1, 2). \)
Therefore, the line joining the points\( (0, 0)\) and \((-1, 2)\) is perpendicular to the given line.
∴ Slope of the line joining\( (0, 0)\) and \((-1, 2)=\frac{2}{-1}=-2\)
The slope of the given line is m.
\(∴ m\times-2=-1\) [The two lines are perpendicular]
\(⇒m=\frac{1}{2}\)
Since point \( (-1, 2)\) lies on the given line, it satisfies the equation \(y = mx + c.\)
\(∴ 2=m(-1)+c\)
\(⇒ 2=\frac{1}{2}(-1)+c\)
\(⇒ c = 2+\frac{1}{2} =\frac{ 5}{2}\)
Thus, the respective values of m and c are \(\frac{1}{2}\) and \(\frac{5}{2}\), respectively.