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Question
In the figure given below, the line segment AB meets X-axis at A and Y-axis at B. The point P(-3, 4) on AB divides it in the ratio 2:3. Find the coordinates of A and B.
Solution
Let the coordinates of A and B be (x, 0) and (0, y) respectively.
Given P divides AB is the ratio 2:3,
Using section formula, we have
`-3 = (2 xx 0 + 3 xx x)/(2 + 3)`
`-3 = "3x"/5`
`-15 = 3x`
x = -5
and
`4 = (2 xx y + 3 xx 0)/(2 + 0)`
`4 = "2y"/5`
20 = 2y
y = 10
Thus, the coordinates of A and B are (–5, 0) and (0, 10) respectively.
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