Find the equation of the perpendicular dropped from the point (–1, 2) onto the line joining the points (1, 4) and (2, 3).

Let P = (-1, 2)

Let A and B be the points (1, 4) and (2, 3).

Slope of AB = $\dfrac{y$2 - y1}{x2 - x1} = \dfrac{3 - 4}{2 - 1} = \dfrac{-1}{1} = -1

We know that,

Product of slope of perpendicular lines is -1.

Let slope of line through P and perpendicular to AB be m.

∴ m × Slope of AB = -1

⇒ m × -1 = -1

⇒ -m = -1

⇒ m = 1.

By point-slope form,

Equation of line through P,

⇒ y - y₁ = m(x - x₁)

⇒ y - 2 = 1[x - (-1)]

⇒ y - 2 = 1(x + 1)

⇒ y - 2 = x + 1

⇒ y - x = 1 + 2

⇒ y - x = 3

⇒ x - y + 3 = 0.

Hence, equation of the perpendicular dropped from the point (-1, 2) onto the line joining the points (1, 4) and (2, 3) is x - y + 3 = 0.