Find the coordinates of the foot of perpendicular from the point (–1, 3) to the line 3x – 4y – 16 = 0.

Let the co-ordinates of the foot of the perpendicular from (-1, 3) to the line 3x – 4y – 16 = 0 be (a, b)

Let the slope of the line joining (-1, 3) and (a, b) be m₁

Let the slope of the line 3x – 4y – 16 = 0 be m₂

∴

Since these two lines are perpendicular m₁ × m₂ = -1

⇒ 3b – 9 = -4a – 4

⇒ 4a + 3b = 5 …….(1)

Point (a, b) lies on the line 3x – 4y = 16

∴ 3a – 4b = 16 ……..(2)

Solving equations (1) and (2), we obtain

a = 68/25 and b = -49/25

Co-ordinates of the foot of perpendicular is (68/25, -49/25)