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In what ratio does the line `y-x+2=0` cut the line joining (3, -1) and (8, 9) ?A. `2 : 3`B. `3 : 2`C. `3 : -2`D. `1 : 2`

Answer» Correct Answer - A
Let the point of intersection divide the line segment joining points, (3, -1) and (8, 9) in K : 1 ratio then :
Then point is `((8k+3)/(k+1), (9k-1)/(k+1))`
Since this point lies on the line `y-x+2=0`
We have, `(9k-1)/(k+1)-(8k+3)/(k+1)+2=0`
`=(9k-1-8k-3)/(k+1)+2=0=(k-4)/(k+1)+2=0`
`=k-4+2k+2=0=3k-2=0`
`k=2/3 : 1` i.e. `2 : 3`


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