In a `Delta ABC, A -= (alpha, beta), B -= (1, 2), C -= (2,3)` and point A lies on the line y = 2 x + 3 where `alpha, beta in l`. If the area of `Delta

Monjur Alahi

In a `Delta ABC, A -= (alpha, beta), B -= (1, 2), C -= (2,3)` and point A lies on the line y = 2 x + 3 where `alpha, beta in l`. If the area of `Delta ABC` be such that `[Delta]=2`, where [.] denotes the greatest integer function, find all possible coordinates of A.
A. `(alpha)/(beta)=3/7`
B. `3alpha beta=14`
C. `2alpha+3beta=18`
D. `alpha+6beta=30`


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Salim Ahmed Kawsar

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Correct Answer - A::C::D
Clearly `R(alpha,beta)` is centroid of `DeltaABC`s
`:.R(alpha,beta)=((3+1+2)/3,(9+2+3)/3)=(2,14/3)`
`impliesalpha=2` and `beta=14/3`
Hence `2alpha+3beta=18`

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