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).
Answer
Reflection of a point (x, y) in the origin gives P'(-x, -y).
Thus, reflection of a P(2, 4) in the origin gives P'(-2, -4).
P'(-2, -4) lies in the third quadrant, where both x and y are negative.
So, assertion (A) is false.
Reflection in the origin preserves distance from the origin.
Both P and P' are at the same distance from the origin:
∴ PO = P'O
So, reason (R) is true.
Thus, Assertion (A) is false, but Reason (R) is true.
Hence, option 2 is the correct option.
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).
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.
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).
Answer
We know that,
The y-coordinate of any point on x-axis equals to 0.
Substituting y = 0 into the equation 3x - 5y = 3, we get :
⇒ 3x - 5.0 = 3
⇒ 3x = 3
⇒ x = = 1
So the point of intersection is P(1, 0).
So, reason (R) is false.
A point is invariant with respect to a line if it lies on that line.
Since, P is the point of intersection of line 3x - 5y = 3 and x-axis, so it lies on line 3x - 5y = 3.
So, assertion (A) is true.
Thus, Assertion (A) is true, but Reason (R) is false.
Hence, option 1 is the correct option.
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.
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).
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.