Mathematics
Assertion (A): The point (6, 3) is invariant when reflected in the line x = 6.
Reason (R): A point M(a, y) is invariant on the line x = a.
A is true, R is false.
A is false, R is true.
Both A and R are true.
Both A and R are false.
Answer
The line of reflection is x = 6.
The point is (6, 3).
Since the x-coordinate of the point (6) is equal to the constant defining the line (x = 6), the point lies on the line of reflection.
A point is invariant on reflection in the line on which it lies.
Assertion is true.
Since the line x = a is a vertical line, any point whose x-coordinate is 'a' lies on this line. Thus, point M(a, y) lies on it.
Thus, point M is invariant on the line x = a.
Reason is true.
Both A and R are true.
Hence, option 3 is the correct option.
Related Questions
Which of the following points is invariant with respect to the line y = -2?
(2, 3)
(-3, 2)
(-2, 3)
(3, -2)
The coordinates of the point P(-3, 5) on reflecting on the x-axis are :
(3, 5)
(-3, -5)
(3, -5)
(-3, 5)
Assertion (A): The point (0, 7) is invariant under the reflection in y-axis.
Reason (R): The image of a point P(x, y) when reflected in the y-axis is P'(-x, y).
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false
Assertion (A): The reflection of the point A(-4, 2) in the origin is the point A'(4, 2).
Reason (R): The image of a point P(x, y) when reflected in the origin is P'(-x, -y).
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false