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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).


Solution

Let A = (1, 4), B = (2, 3), and C = (-1, 2).

Slope of AB = fraction numerator 3 minus 4 over denominator 2 minus 1 end fraction equals negative 1

Slope of equation perpendicular to AB = fraction numerator negative 1 over denominator s l o p e space o f space A B end fraction equals 1

The equation of the perpendicular drawn through C onto AB is given by:

y - y1 = m(x - x1)

y - 2 = 1(x + 1)

y - 2 = x + 1

y = x + 3

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