Published by:
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 number of all possible coordinates of A.
Text Solution
Verified by ExpertsThe correct answer is:
0004
Ans. 0004
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
⇒ Hence A has 4 coordinates.
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
The polar coordinates of (2, –2) will be–
The straight line joining the points, (1, 2) and (–2, 1) is divided by the line 3x + 4y = 7 in the …
The line segment joining the points (–3, –4) and (1, –2) is divided by y-axis in the ratio-
If the distance between the points (a, 2) and (3, 4) be 8, then a =
If the points A(6, – 1), B(1, 3) and C (x, 8) be such that AB = BC, then x=
The mid points of sides of a triangle are (2, 1), (–1, –3) and (4, 5). Then the coordinates of its …