Question

The line joining the points A (–3, –10) and B (–2, 6) is divided by the point P such that `(PB)/(AB) = 1/5`. Find the co-ordinates of P.

Answer 1

Let the co-ordinates of P be (x, y) which divides the line joining the points A (–3, –10) and B (–2, 6) in the ratio of AP : PB i.e. (5 – 1) : 1 or 4 : 1

Since 5 PB = PA + PB

`\implies` 4 PB = PA

`\implies (PA)/(PB) = 4/1`

∴ `x = (4 xx (-2) + 1 xx (-3))/(4 + 1)`

= `(-8 - 3)/5`

= `(-11)/5`

`y = (4 xx 6 + 1 xx (-10))/(4 + 1)`

= `(24 - 10)/5`

= `14/5`

∴  Co-ordinates of P are `((-11)/5, 14/5)`