Question

A line through point P(4, 3) meets x-axis at point A and the y-axis at point B. If BP is double of PA, find the equation of AB.

Answer 1

Since a line through point P meets x-axis at point A and at point B,

Co-ordinates of A are (x, 0) and Co-ordinates of B are (0, y). 

Now, BP = 2PA 

`=> (BP)/(PA) = 2/1`

`=>` P divides AB in the ratio 2 : 1

So, the co-ordinates of P are `((2 xx x + 1 xx 0)/(2 xx 1),(2 xx 0 + 1 xx y)/(2 xx 1)) = ((2x)/3, y/3)`

But, co-ordinates of P are (4, 3)

`=> 2x/3 = 4`

`=>` 2x = 12

`=>` x = 6

And `y/3 = 3`

`=>` y = 9

`=>` Co-ordinates of A are (6, 0) and co-ordinates of B are (0, 9)

∴ Slope of line AB = `(9 - 0)/(0 - 6) = 9/(-6) = -3/2`

Thus, the equation of line AB is given by

`y - 0 = -3/2(x - 6)`

i.e 2y = 3x + 18 

i.e 3x + 2y = 18