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If the points A(-1,-4),B(b,c)and C(5,-1)...

If the points `A(-1,-4),B(b,c)and C(5,-1)` are collinear and 3b + c = 4, find the values of b and c.

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Points `A(-1,-4),B(b,c)andC(5,-1)` are collinear
`therefore" ""area of"DeltaABC=0`
`implies" "-1(c+1)+b(-1+4)+5(-4-c)=0`
`implies" "-c-1+3b-20-5c=0`
`implies" "3b-6c=21`
`implies" "b-2c=7" "...(1)`
`"Given that,"2b+c=4" "...(2)`
from eqs. (1) and (2), we get
`b=3andc=2`
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