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CGP EDU Academic Team
Published on: August 14, 2026
The line 2x + 3y = 12 meets the x-axis at A and
y-axis at B. The line through (5, 5) perpendicular to AB meets the x-axis, y-axis and the AB at C, D and E respectively. If O is the origin of coordinates, then the area of OCEB is :
Text Solution
Verified by ExpertsThe correct answer is:
C
2x + 3y = 12 … (i)
x/6 + y/4 = 1 ⇒ A(6, 0), B(0, 4)
A line perpendicular to (i)
⇒ 3x – 2y + λ = 0
Passes through (5, 5) ⇒ λ = – 5
⇒ line is 3x – 2y = 5 …(ii)
C ≡ (5/3, 0) D ≡ (0, –5/2)
Pt. of intersection of (i) and (ii) is E(3, 2)
⇒ O(0, 0), C(5/3, 0), E(3, 2), B(0, 4)
Now area of quadrilateral OCEB
= 
= 
= 23/3
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