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Coordinate Geometry
CH07 Question Bank
CBSE_CH07_QUESTION_BANK
Grade 10
Question:
Assertion (A): The points $(1,1),(2,2),(3,3)$ are collinear. Reason (R): Three points are collinear if the sum of the distances between two pairs of them equals the distance between the remaining (outer) pair.
Both Assertion (A) and Reason (R) are true, and R is the correct explanation of A. Both Assertion (A) and Reason (R) are true, but R is NOT the correct explanation of A. Assertion (A) is true, but Reason (R) is false. Assertion (A) is false, but Reason (R) is true.
Step-by-Step Solution
Key Concept: Direct verification using the distance-based collinearity test.
$AB=\sqrt2,\ BC=\sqrt2,\ AC=2\sqrt2$; since $AB+BC=AC$, the points are collinear — A is true. [0.5 Mark]
R correctly states the exact test used to confirm A, so R correctly explains A. [0.5 Mark]
Correct Answer:Both Assertion (A) and Reason (R) are true, and R is the correct explanation of A.
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