In which quadrant the point P that divides the line segment joining the points A (2, -5) and B (5, 2) in the ratio 2 : 3 lies?

We have to find the coordinates of the point P.

x-coordinate of P = (n₁x₂ + n₂x₁ )/n₁ + n₂

where n₁ : n₂ is the ratio in which line is to be divided and,
x₁ and x₂ are the x- coordinates of the points, A and B respectively.

∴ x-coordinate of P = ( 2 × 5 + 3 × 2)/ 2 + 3

= 16/5

Similarly y-coordinate of P = (n₁y₂ + n₂y₁ )/n₁ + n₂

where n₁ : n₂ is the ratio in which line is to be divided and,
y₁ and y₂ are the x- coordinates of the points, A and B respectively.

∴ y-coordinate of P = ( 2 × 2 + 3 × -5 )/ 2 + 3

= -11/5

Coordinate of P =(16/5 , -11/5)

∴ It lies in the fourth quadrant.