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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Answer
Let P = (-1, 2)
Let A and B be the points (1, 4) and (2, 3).
We know that,
Product of slope of perpendicular lines is -1.
Let slope of line through P 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
⇒ y = x + 3
Hence, equation of the perpendicular dropped from the point (-1, 2) onto the line joining the points (1, 4) and (2, 3) is y = x + 3.
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