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Coordinate Geometry
CH07 Question Bank
CBSE_CH07_QUESTION_BANK
Grade 10
Question:
Assertion (A): If the distance between $(x,0)$ and $(0,y)$ is $10$, then $x^2+y^2=100$. Reason (R): By the distance formula, $[\text{distance}]^2=(x-0)^2+(0-y)^2=x^2+y^2$.
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 algebraic substitution into the distance formula.
Squaring both sides of the given distance condition: $100=x^2+y^2$ — A is true. [0.5 Mark]
R correctly derives exactly this relation from the distance formula, 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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