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Question
Answer the following question:
A line perpendicular to segment joining A(1, 0) and B(2, 3) divides it internally in the ratio 1 : 2. Find the equation of the line.
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Solution
Let P(x, y) be the point which divides AB internally in the ratio 1 : 2, where A(1, 0) and B(2, 3).
∴ x = `(1(2) + 2(1))/(1 + 2) = (2 + 2)/3 = 4/3`
and y = `(1(3) + 2(0))/(1 + 2) = (3 + 0)/3` = 1
∴ P ≡ `(4/3, 1)`
Now, slope of AB = `(3 - 0)/(2 - 1)` = 3
∴ slope of the line perpendicular to AB is `-1/3` and it is passing through `"P"(4/3, 1)`.
∴ equation of the required line is
y – 1 =`-1/3(x - 4/3)`
∴ 3y – 3 = `- x + 4/3`
∴ x + 3y = `13/3`
∴ 3x + 9y = 13
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