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In a Delta ABC, A -= (alpha, beta), B -=...

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`

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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