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Solve the following questions. (Any two ...

Solve the following questions. (Any two )
(iv) Find the ratio in which point P (k,7) divides the segment joining A (8,9) and B (1,2) . Also find k.

Text Solution

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`A(8,9),B(1,2)` and `P(k,8)`.
Let P divide the seg AB in the ratio `m:n`
By section formula.
`7=(m(2)+n(9))/(m+n)`
`:.7=(2m+9n)/(m+n)`
`:.7(m+n)=2m+9n`
`:.7m+7n=2m+9n`
`:.7m-2m=9n-7n`
`:.5m=2n`
`:.m/n=2/5`
`:.m:n=2:5`
P divides segment AB in the ratio `2:5`
By section formula.
`k=(2(1)+5(8))/(2+5), :.k=(2+40)/7`
`:.k=42/7`
`k=6`.
The ratio in which point P divides seg AB is `2:5` and value of k is 6.
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