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In what ratio does the point (( 24)/(11)...

In what ratio does the point `(( 24)/(11) , y)` divide the line segment joining the points `P(2, -2) and Q(3, 7)`? Also find the value of y.

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Let M `((24)/(11), y)` divide the line segment joining the points

`P(2, -2) and Q(3, 7)` in the ratio `k:1`.
`therefore" "(24)/(11)=(k(3)+1(2))/(k+1)" "` (by using section formula)
`rArr" "11(3k+2)=24(k+1) rArr" "33k+22=24k +24`
`rArr" "33k-24k = 24-22rArr" "9k=2`
`therefore" "k=(2)/(9)`
`therefore` Required ratio = `k:1`
`i.e., " "(2)/(9):1`
`i.e., " "2:9` internally.
`therefore ` Required ratio = 2: 9
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