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Question
In what ratio does the point (1, a) divide the join of (–1, 4) and (4, –1)? Also, find the value of a.
Solution
Let the point P (1, a) divides the line segment AB in the ratio k : 1.
Using section formula, we have:
`1 = (4k - 1)/(k + 1)`
`=> k + 1 = 4k - 1`
`=> 2 = 3k`
`=> k = 2/3` ...(1)
`=>a = (-k + 4)/(k + 1)`
`=> a = (-2/3 + 4)/(2/3 + 1)` ...(From 1)
`=> a = 10/5 = 2`
Hence, the required is 2 : 3 and the value of a is 2.
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