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In a ` A B C ,A-=(alpha,beta),B-=(1,2),C-=(2,3),` point `A` lies on the line `y=2x+3,` where `alpha,beta` are integers, and the area of the triangle is `S` such that `[S]=2` where `[` .`]` denotes the greatest integer function. Then the possible coordinates of `A` can be `(-7,-11)` (b) `(-6,-9)` `(2,7)` (d) `(3,9)`

A

`(alpha)/(beta)=3/7`

B

`3alpha beta=14`

C

`2alpha+3beta=18`

D

`alpha+6beta=30`

Text Solution

Verified by Experts

The correct Answer is:
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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