How do I find the image of O (0,0) after two reflections, first across x=a and then across y=b?
h5 gj 5f
To find the image of point O(0,0) after two reflections, first across the line x=a and then across the line y=b, you can follow these steps:
1. Reflect point O across the line x=a:
- The line x=a acts as a mirror. The distance between O and the line x=a is |a - 0| = |a|.
- Therefore, the x-coordinate of the reflected point is given by 2a - 0 = 2a.
- The y-coordinate remains the same since the point is reflected only across the x-axis.
- So, the reflected point after the first reflection is (2a, 0).
2. Reflect the resulting point (2a, 0) across the line y=b:
- The line y=b acts as another mirror. The distance between the previous point (2a, 0) and the line y=b is |b - 0| = |b|.
- Therefore, the y-coordinate of the reflected point is given by 2b - 0 = 2b.
- The x-coordinate remains the same since the point is reflected only across the y-axis.
- So, the final image after both reflections is (2a, 2b).
In summary, the image of point O(0,0) after reflecting it first across x=a and then across y=b is (2a, 2b).
reflection through x=a moves (x,y) -> (a-(x-a),y)
Similarly for y=b.
So,
(0,0) -> (2a,0) -> (2a,2b)