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Question
In what ratio does the point (a, 6) divide the join of (–4, 3) and (2, 8)? Also, find the value of a.
Solution
Let the point P (a, 6) divides the line segment joining A (–4, 3) and B (2, 8) in the ratio k : 1.
Using section formula, we have:
`6 = (8k + 3)/(k + 1)`
`=> 6k + 6 = 8k + 3`
`=>3 = 2k`
`=> k = 3/2` ...(1)
`=>a = (2k - 4)/(k + 1)`
`=>a = (2 xx 3/2 - 4)/(3/2 + 1)` ...(From 1)
`=> a = -2/5`
Hence, the required ratio is 3 : 2 and the value of a is `-2/5`
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