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.

Answer 1

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