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CGP EDU Academic Team
Published on: August 14, 2026
In a Δ ABC, A ≡ ( α, β ), B ≡ (1, 2), C ≡ (2, 3) and Point ‘A’ lies on the line y = 2x + 1 where α, β ∈ integer. Area of triangle ABC is Δ such that [ Δ ] =2, where [.] denotes greatest integer function. Find all possible coordinate of A.
Text Solution
Verified by ExpertsThe correct answer is:
2
Sol. A( α, β ) lies on y = 2x + 1 ⇒ A = ( α , 2 α + 1) Clearly BC = 
and equation of BC is y = x + 1
Now distance of A from BC = 
. Thus area of
Δ ABC = 
. 
. 
= 
Hence, 2 ≤ 
< 3 ⇒ α ∈ ( –6, –4] ∪ [4, 6)
Since ‘ α ’ is an integer ⇒ α = –5, –4, 4, 5
∴ A ≡ (–5, –9) (–4, –7), (4, 9), (5, 11)
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