Mathematics
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).
Reflection
2 Likes
Answer
A point is invariant with respect to a line if lies on the line.
So, if a point is invariant under reflection over y = 2, it must lie on the line y = 2.
So, reason (R) is true.
If P(-5, m) is invariant under reflection over y = 2, so it lies on the line y = 2, so m = 2.
So, assertion (A) is false.
Thus, Assertion (A) is false, but Reason (R) is true.
Hence, option 2 is the correct option.
Answered By
1 Like
Related Questions
Which of the following points is invariant with respect to the line y = -2?
(3, 2)
(3, -2)
(2, 3)
(-2, 3)
P(2, 4) is a point in first quadrant.
Assertion (A): Its reflection P' in origin O is in 2nd quadrant.
Reason (R): PO = P'O
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).
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).