Mathematics
A point is invariant with respect to both x-axis and y-axis.
Assertion (A): It is invariant with respect to origin also.
Reason (R): The point is origin itself.
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).
Reflection
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Answer
We know that,
Point invariant to both x-axis and y-axis is their point of intersection i.e. the origin.
So, assertion (A) is true.
A point is invariant to itself.
So, reason (R) is true.
Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).
Hence, Option 3 is the correct option.
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Related Questions
P is the point of intersection of the line 3x - 5y = 3 and x - axis.
Assertion (A): P is invariant with respect to given line.
Reason (R): Coordinates of P are (0, 1).
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).
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Assertion (A): Area (Δ ABC) = Area (Δ A'B'C').
Reason (R): The two triangles are congruent.
Assertion (A) is true, but Reason (R) is false.
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Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).
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