Question

P (1, −2) is a point on the line segment joining points A (3, −6) and B (x, y). If P divides AB in the ratio 2 : 3, find the coordination of B.

Answer 1

If P divides AB in the ratio AP : PB = m:n,

Then P = `((nxA + mxB) / (m + n), (nyA + myB) / (m + n))`

Here,

m = 2, n = 3,

A = (3, −6), B = (x, y),

P = (1, −2),

So,

⇒ `(9 + 2x) / 5 = 1`

2x + 9 = 5

∴ x = −2,

⇒ `(−18 + 2y) / 5 = -2`

2y − 18 = −10

∴ y = 4

Hence, B = (−2, 4).