Invariant Points for Reflection in a Line

If the point P is on the line AB then clearly its image in AB is P itself. We say P is an invariant point for the axis of reflection AB.

Thus, all the points lying on a line are invariant points for reflection in that line and no points lying outside the line will be an invariant point.


Solved examples on invariant points for reflection in a line:

1. Which of the following points (-2, 0), (0, -5), (3, -3) are invariant points when reflected in the x-axis?   

We know that only those points which lie on the line are invariant points when reflected in the line. So, only those points are invariant which lie on the x-axis. Hence, the invariant points must have y-coordinate = 0. Therefore, only (-2, 0) is the invariant point.


2. Which of the following points (7, 0), (-1, 1), (2, 2), (0, 4) are invariant points when reflected in the x-axis?  

We know that only those points which lie on the line are invariant points when reflected in the line. So, only those points are invariant which lie on the y-axis. Hence, the invariant points must have x-coordinate = 0. Therefore, only (0, 4) is the invariant point.


3. Which of the following points (-4, 3), (0, 4), (4, -1), (-3, 4) are invariant points when reflected in the line parallel to the x-axis at a distance 4 on the positive side of the y-axis?  

We know that only those points which lie on the line are invariant points when reflected in the line. So, only those points are invariant which are on the line parallel to the x-axis at a distance 4 on the positive side of the y-axis. Hence, the invariant points must have y-coordinate = 4. Therefore, (0, 4) and (-3, 4) are the invariant points.




10th Grade Math

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