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Question
For what value of a point (a, 1), (1, -1) and (11, 4) are collinear?
Solution
Let A(a,1), B(1,-1) and (11,4) be the given point
Area of ΔABC
`=1/2{a(-1-4)+1(4-1)+11(1+1)} `
`=1/2 {-5+3+22}`
`1/2{-5a+25}`
for the point to be collinear
Area of ΔABC=20
`1/2{-5a+25}=0`
`=>-5a+25=0`
`=>-5a=-25`
`=>a=5`
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