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.

The perpendicular from the origin meets the given line at (–1, 2).

The equation of line is y = mx + c

The line joining the points (0, 0) and (–1, 2) is perpendicular to the given line.

So, the slope of the line joining (0, 0) and (–1, 2) 

= \(- \dfrac{2}{1}\) = -2

Slope of the given line is m.

m × (-2) = -1

m = \( \dfrac{1}{2}\)

Since, point (-1, 2) lies on the given line,

y = mx + c

2 = \( \dfrac{1}{2}\) × (-1) + c

c = 2 + \( \dfrac{1}{2}\) = \( \dfrac{5}{2}\)

The values of m and c are \( \dfrac{1}{2}\) and \( \dfrac{5}{2}\) respectively.