Question:
What is the area of the triangle formed joining the points A, B and C?
I) $A=(2,5), B=(3,2)$
II) A, B and C lie on a straight line
What is the area of the triangle formed joining the points A, B and C?
I) $A=(2,5), B=(3,2)$
II) A, B and C lie on a straight line
Show Hint
Collinear points always form a triangle with an area of zero.
Updated On: Jul 3, 2026
- Statement I alone is sufficient to answer the question
- Statement II alone is sufficient to answer the question
- Both the statements I and II are sufficient to answer the question but neither statement alone is not sufficient
- Both the statements I and II together are not sufficient to answer the question and additional data is required
Show Solution
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The Correct Option is B
Solution and Explanation
Step 1: Concept
In coordinate geometry, the area of a triangle is zero if the three points forming it are collinear (lie on a straight line).
Step 2: Meaning
Statement I only gives coordinates for two points, which is insufficient to determine the position of point C.
Step 3: Analysis
Statement II explicitly states that A, B, and C are collinear. This definitionally means the area of the triangle formed by them is zero.
Step 4: Conclusion
Therefore, Statement II alone provides a definitive answer (Area = 0) regardless of the specific coordinates. Final Answer: (B)
In coordinate geometry, the area of a triangle is zero if the three points forming it are collinear (lie on a straight line).
Step 2: Meaning
Statement I only gives coordinates for two points, which is insufficient to determine the position of point C.
Step 3: Analysis
Statement II explicitly states that A, B, and C are collinear. This definitionally means the area of the triangle formed by them is zero.
Step 4: Conclusion
Therefore, Statement II alone provides a definitive answer (Area = 0) regardless of the specific coordinates. Final Answer: (B)
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