Question

The point P(x, y) divides the line segment joining the points A(−1, 3) and B(9, 8) such that AP : PB = k : 1. If the coordinates of P are such that x = y, then find the value of k.

Answer 1

Using the section formula to find the coordinates of point P.

x = `(9k + (-1))/(k + 1)`

= `(9k - 1)/(k + 1)`

and y = `(8k + 3)/(k + 1)`

Since, point P lies on the line x − y = 0, so it will satisfy the equation.

∴ x − y = 0

∴ `(9k - 1)/(k + 1) - (8k + 3)/(k + 1) = 0`

∴ `(9k - 1 - 8k - 3)/(k + 1) = 0`

∴ k − 4 = 0

∴ k = 4

Hence, the value of k is 4.