In the given figure, line APB meets the x-axis at point A and y-axis at point B. P is the point (-4, 2) and AP : PB = 1 : 2. Find the co-ordinates of A and B.

Since, A lies on x-axis its co-ordinates be (x, 0) and B lies on y-axis its co-ordinates be (0, y).

Given, AP : PB = 1 : 2.

By section formula,

$x = \dfrac{m$1x2 + m2x1}{m1 + m2} \\[1em] \Rightarrow -4 = \dfrac{1 \times 0 + 2 \times x}{1 + 2} \\[1em] \Rightarrow -4 \times 3 = 2x \\[1em] \Rightarrow 2x = -12 \\[1em] \Rightarrow x = -6. \\[1em] y = \dfrac{m1y2 + m2y1}{m1 + m2} \\[1em] \Rightarrow 2 = \dfrac{1 \times y + 2 \times 0}{1 + 2} \\[1em] \Rightarrow 2 \times 3 = y \\[1em] \Rightarrow y = 6.

A = (x, 0) = (-6, 0) and B = (0, y) = (0, 6).

Hence, A = (-6, 0) and B = (0, 6).