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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Related Questions
The point P(-4, -5) on reflection in y-axis is mapped on P'. The point P' on reflection in the origin is mapped on P''. Find the coordinates of P' and P''. Write down a single transformation that maps P onto P''.
A point P(a, b) is reflected in the x-axis to P'(2, -3), write down the values of a and b. P'' is the image of P, when reflected in the y-axis. Write down the coordinates of P''. Find the coordinates of P''', when P is reflected in the line, parallel to y-axis such that x = 4.
Write down the coordinates of the image of the point (3, -2) when:
(i) reflected in the x-axis.
(ii) reflected in the y-axis.
(iii) reflected in the x-axis followed by reflection in the y-axis.
(iv) reflected in the origin.
If P'(-4, -3) is the image of a point P under reflection in the origin, find
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(ii) the coordinates of the image of P under reflection in the line y = -2.