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.

Given equation of line is y = mx + c

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) = 2/(-1) = -2

Slope of the given line is m.

m × (-2) = -1

∴ m = 1/2

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

y = mx + c

⇒ 2 = 1/2 × (-1) + c

⇒ c = 2 + 1/2 = 3/2

The respective values of m and c are 1/2 and 5/2 respectively.