The point P(5, -4) divides the line segment AB, as shown in the figure, in the ratio 2 : 5. Find the co-ordinates of points A and B. Given AP is smaller than BP.

Since, A is on x-axis, let it co-ordinates be (a, 0) and B is on y-axis so it's co-ordinates (0, b).

By formula,

$x = \dfrac{m$1x2 + m2x1}{m1 + m2} \\[1em] \Rightarrow 5 = \dfrac{2 \times 0 + 5 \times a}{2 + 5} \\[1em] \Rightarrow 5 \times 7 = 0 + 5a \\[1em] \Rightarrow 5a = 35 \\[1em] \Rightarrow a = \dfrac{35}{5} = 7 \\[1em] y = \dfrac{m1y2 + m2y1}{m1 + m2} \\[1em] \Rightarrow -4 = \dfrac{2 \times b + 5 \times 0}{2 + 5} \\[1em] \Rightarrow -4 \times 7 = 2b + 0 \\[1em] \Rightarrow 2b = -28 \\[1em] \Rightarrow b = -14.

∴ A = (a, 0) = (7, 0) and

B = (0, b) = (0, -14).

Hence, A = (7, 0) and B = (0, -14).