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.
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.
Reflection
1 Like
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.
Answered By
1 Like
Related Questions
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.
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.
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.
ABC is a triangle as shown in the figure below.
(a) Write down the coordinates of A, B and C on reflecting through the origin.
(b) Write down the coordinates of the point/s which remain invariant on reflecting the triangle ABC on the x-axis and y-axis respectively.