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Question
A line segment joining A`(-1,5/3)` and B(a, 5) is divided in the ratio 1 : 3 at P, the point where the line segment AB intersects the y-axis.
- Calculate the value of ‘a’.
- Calculate the co-ordinates of ‘P’.
Solution
Since, the line segment AB intersects the y-axis at point P, let the co-ordinates of point P be (0, y).
P divides AB in the ratio 1 : 3.
∴ `(0, y) = ((1 xx a + 3 xx (-1))/(1 + 3),(1 xx 5 + 3 xx 5/3)/(1 + 3))`
`(0, y) = ((a - 3)/(4),10/4)`
`0 = (a - 3)/4` and `y = 10/4`
`a = 3` and `y = 5/2 = 2 1/2`
Thus, the value of a is 3 and the co-ordinates of point P are `(0, 2 1/2)`
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