Straight Lines
The straight line 4x + 3y - 24 = 0 forms a triangle with the two coordinate axes; what is the area of this triangle measured in square units?
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About This Question
- Subject
- mathematics
- Chapter
- coordinate geometry
- Topic
- straight lines
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
24
A line crossing both axes bounds a right triangle with the axes whose legs are the magnitudes of the x- and y-intercepts, so finding those intercepts immediately gives the area. Setting y = 0 in 4x + 3y - 24 = 0 gives 4x = 24, so x = 6, the x-intercept. Setting x = 0 gives 3y = 24, so y = 8, the y-intercept. The triangle has legs 6 and 8 along the axes, so its area is (1/2)(6)(8) = 24 square units. Option 48 forgets the factor of one-half. Option 12 halves one leg erroneously. Option 36 mistakes the legs as 6 and 12. This applies the standard JEE Advanced intercept-triangle area method. Plausibility check: the right angle sits at the origin between the positive intercepts 6 and 8, and (1/2)(6)(8) = 24 is consistent with a moderate triangle entirely in the first quadrant, confirming the geometry.
This easy difficulty mathematics question is from the chapter coordinate geometry, covering the topic of straight lines. It appeared in the 2025 exam.
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