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).
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.
Related Questions
P(-5, m) is invariant with respect to y = 2.
Assertion (A): Value of m is -2.
Reason (R): P lies on y = 2.
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).
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).
Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).
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).
The point P(4, -7) on reflection in x-axis is mapped onto P'. Then P' on reflection in the y-axis is mapped onto P''. Find the coordinates of P' and P''. Write down a single transformation that maps P onto P''.