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Question
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.
Solution
Given, A lies on x-axis and B lies on y-axis.
Let the co-ordinates of A and B be (x, 0) and (0, y) respectively.
Given, P is the point (−4, 2) and AP : PB = 1 : 2.
Using section formula, we have:
`-4 = (1 xx 0 + 2 xx x)/(1 + 2)`
`-4 = (2x)/3`
`x = (-4 xx 3)/2 = -6`
Also,
`2 = (1 xx y + 2 xx 0)/(1 + 2)`
`2 = y/3`
`y = 6`
Thus, the co-ordinates of points A and B are (−6, 0) and (0, 6) respectively.
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