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Question
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.
Solution
From the figure, the line AB intersects x-axis at A and y-axis at B.
Let the co-ordinates of A (x, 0) and B (0, y) and P (5, –4) divides it in the ratio of 2 : 5
∴ `5 = (2 xx 0 + 5 xx x)/(2 + 5)`
`5 = (0 + 5x)/7`
∴ 5x = 35
`x = 35/5`
x = 7
Again, `-4 = (2 xx y + 5 xx 0)/(2 + 5)`
`-4 = (2y + 0)/7`
∴ 2y = –4 × 7 = –28
`y = (-28)/2`
y = –14
∴ Co-ordinates of A are (7, 0) and of B are (0, –14)
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