Point P divides join of points A = (0, -5) and B = (10, -5) internally in the ratio 3 : 2 such that the point P is nearer to point A. The co-ordinates of point P are :

1. (4, 0)

2. (0, -5)

3. (-4, -5)

4. (4, -5)

Given,

Point P is nearer to point A.

∴ AP : BP = 2 : 3

By section formula,

(x, y) = $\dfrac{m$1x2 + m2x1}{m1 + m2}

Let coordinates of P be (x, y).

Substituting values we get :

$\Rightarrow (x, y) = \Big(\dfrac{2 \times 10 + 3 \times 0}{2 + 3}, \dfrac{2 \times -5 + 3 \times -5}{2 + 3}\Big) \\[1em] \Rightarrow (x, y) = \Big(\dfrac{20 + 0}{5}, \dfrac{-10 - 15}{5}\Big) \\[1em] \Rightarrow (x, y) = \Big(\dfrac{20}{5}, \dfrac{-25}{5}\Big) \\[1em] \Rightarrow (x, y) = (4, -5)$

Hence, Option 4 is the correct option.