Final answer:
To write a rule for reflection in a coordinate plane, flip the coordinates across a line of reflection; over the x-axis, change the y-coordinate to its opposite; over the y-axis, change the x-coordinate to its opposite; and over the lines y = x or y = -x, swap the coordinates or swap and negate them, respectively.
Step-by-step explanation:
The question asks for a rule for reflection. A reflection in mathematics is a transformation that flips a figure across a line, creating a mirror image of the original figure. The line across which the figure is flipped is known as the line of reflection.
Rules for Reflection
For a reflection in a coordinate plane:
- Reflections over the x-axis: If a point has coordinates (a, b), then its reflection across the x-axis has coordinates (a, -b).
- Reflections over the y-axis: If a point has coordinates (a, b), then its reflection across the y-axis has coordinates (-a, b).
- Reflections over the line y = x: If a point has coordinates (a, b), then its reflection across the line y = x has coordinates (b, a).
- Reflections over the line y = -x: If a point has coordinates (a, b), then its reflection across the line y = -x has coordinates (-b, -a).
These rules can be applied to individual points as well as to figures composed of multiple points. The key to performing a reflection is to always maintain the distance and angle from the line of reflection consistent for all points of the figure being reflected.