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).
Both A and R are true, and R is the correct explanation of A.
Both A and R are true, but R is not the correct explanation of A.
A is true, but R is false.
A is false, but R is true.
Answer
Since, x-coordinate of point (0, 7) is 0, thus it lies on y-axis.
A point is invariant on reflection in the line on which it lies.
∴ Assertion (A) is true.
On reflection in y-axis,
The y-coordinate remains same and the sign of x-coordinate changes.
Thus, P(x, y) when reflected in the y-axis becomes P'(-x, y).
∴ Reason (R) is false.
Hence, option 3 is the correct option.
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).
Both A and R are true, and R is the correct explanation of A.
Both A and R are true, but R is not the correct explanation of A.
A is true, but R is false.
A is false, but R is true.
Answer
Rule to find reflection of a point in origin :
Change the sign of abscissa i.e. x-coordinate and ordinate i.e. y-coordinate.
A(-4, 2) ⇒ A'(4, -2)
Assertion (A) is false.
Reflection in the origin requires changing the sign of both the x-coordinate and the y-coordinate.
Thus,
P(x, y) ⇒ P'(-x, -y)
Reason (R) is true.
A is false, R is true.
Hence, option 4 is the correct option.
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.
Both A and R are true, and R is the correct explanation of A.
Both A and R are true, but R is not the correct explanation of A.
A is true, but R is false.
A is false, but R is true.
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 (A) 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 (R) is true.
Both A and R are true, and R is the correct explanation of A.
Hence, option 1 is the correct option.
Assertion (A): The point (-2, 8) is invariant under reflection in line x = -2.
Reason (R): If a point has its x-coordinate 0, it is invariant under refelection in both axes.
Both A and R are true, and R is the correct explanation of A.
Both A and R are true, but R is not the correct explanation of A.
A is true, but R is false.
A is false, but R is true.
Answer
Reflection in the line x = -2 means the mirror line passes through x = -2. Any point lying on that line will remain unchanged after reflection.
Therefore, after reflection the point remains (-2, 8).
Assertion (A) is True.
Let us consider a point (0, y):
On reflection in y-axis, the sign of x-coordinate changes,
(0, y) ⇒ (0, y)
On reflection in x-axis, the sign of y-coordinate changes,
(0, y) ⇒ (0, -y).
So it is not invariant under both axes.
Reason (R) is false.
A is true, R is false.
Hence, option 3 is the correct option.