Mathematics
Which of the following points is invariant with respect to the line y = -2?
(2, 3)
(-3, 2)
(-2, 3)
(3, -2)
Answer
The line of reflection is y = -2.
The point is (3, -2).
Since the y-coordinate of the point (-2) is equal to the constant defining the line (y = -2), the point lies on the line of reflection.
A point is invariant on reflection in the line on which it lies.
Hence, Option 4 is the correct option.
Related Questions
If the point A(m, n) is first reflected in the y-axis and then reflected in the x-axis to the point A"(-10, 15), then the value of (m - n) is :
-25
-5
5
25
The reflection of the point (-5, 0) in the origin is :
(-5, 0)
(0, -5)
(5, 0)
(0, 5)
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