In the given figure, the line segment AB meets x-axis at A and y-axis at B. The point P(-3, 1) on AB divides it in ratio 2 : 3. Find the coordinates of A and B.

Since, point A and B lies on x-axis and y-axis respectively. Let their coordinates be A(a, 0) and B(0, b).

Given,

The line segment AB be divided by point P(-3, 1) in the ratio AP : PB = 2 : 3.

By section formula,

$\Rightarrow (x, y) = \Big(\dfrac{m$1x2 + m2x1}{m1 + m2}, \dfrac{m1y2 + m2y1}{m1 + m2}\Big) \\[1em] \Rightarrow (-3, 1) = \Big(\dfrac{2(0) + 3(a)}{2 + 3}, \dfrac{2(b) + 3(0)}{2 + 3}\Big) \\[1em] \Rightarrow (-3, 1) = \Big(\dfrac{3a}{5}, \dfrac{2b}{5}\Big) \\[1em] \Rightarrow -3 = \Big(\dfrac{3a}{5}\Big), 1 = \Big(\dfrac{2b}{5}\Big) \\[1em] \Rightarrow -15 = 3a, 5 = 2b \\[1em] \Rightarrow a = \dfrac{-15}{3}, b = \dfrac{5}{2} \\[1em] \Rightarrow a = -5, b = \dfrac{5}{2} \\[1em] \Rightarrow A = (a, 0) = (-5, 0) \\[1em] \Rightarrow B = (0, b) = \Big(0, \dfrac{5}{2}\Big).

Hence, A(-5, 0) and $B\Big(0, \dfrac{5}{2}\Big)$.