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Question
In what ratio does the point (1, a) divided 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.
Coordinates of P are,
`1 = (4"k" - 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 ratio is 2 : 3 and the value of a is 2.
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