Mathematics
Find the coordinates of the image of (3, 1) under reflection in x-axis followed by reflection in the line x = 1.
Reflection
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Answer
We know that,
Rule to find reflection of a point in x-axis :
- Retain the abscissa i.e. x-coordinate.
- Change the sign of ordinate i.e. y-coordinate.
∴ Point P'(3, -1) is the image on reflection of (3, 1) in x-axis.
We know that the reflection of the point (x, y) in the line x = a is the point (-x + 2a, y).
∴ The image of the point P'(3, -1) under reflection in the line x = 1 is the point P'(-3 + 2 × 1, -1) i.e., the point P'(-1, -1).
Hence, the coordinates of the final image is P''(-1, -1).
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