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

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

KnowledgeBoat · Accepted Answer

Let P = (-1, 2) Let A and B be the points (1, 4) and (2, 3). Slope of AB = 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.

Mathematics

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

Straight Line Eq

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