Mathematics
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.
Related Questions
The reflection of the point (-3, 0) in the origin is the point
(0, -3)
(0, 3)
(3, 0)
none of these
Which of the following points is invariant with respect to the line y = -2?
(3, 2)
(3, -2)
(2, 3)
(-2, 3)
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).