Question

Find the ratio in which P(4, m) divides the line segment joining the points A(2, 3) and B(6, –3). Hence find m.

Answer 1

Let P divides AB in a ratio of λ : 1

Therefore, coordinates of the point P are `((6lambda+2)/(lambda + 1), (-3lambda + 3)/(lambda + 1))`

Given that coordinates of the point P are (4, m).

`=> (6lambda + 2)/(lambda + 1) = 4`

`=> 6lambda + 2 = 4lambda +  4`

`=> lambda = 1`

Hence, the point P divides AB in a ratio of 1 : 1.

Replacing the value of λ = 1 in y-coordinate of P, we get

`(-3(1)+3)/(1+1) = m`

`=> m = 0`

Thus, y-coordinate of P is equal to 0.