Mathematics
ABC is a triangle and its vertices A, B, C are reflected in y-axis to the points A', B' and C' respectively.
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.
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
A point (x, y) reflected in the y-axis becomes (−x, y).
This changes the sign of the x-coordinate but preserves the y-coordinate.
As a result, distances and angles are preserved, and so is area.
Reflection over an axis is a rigid transformation (i.e., it preserves size and shape)
Thus, the area remains unchanged.
So, assertion (A) is true.
Since all corresponding sides and angles remain equal under reflection.
Thus, the two triangles are congruent.
So, reason (R) is true and reason (R) is the correct explanation of assertion (A).
Thus, 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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