The algebraic rule for reflection depends on the line (or point) of reflection. Here's a breakdown of common reflections and their corresponding rules based on the provided reference:
Common Reflection Rules
The following table summarizes the algebraic rules for common reflections:
| Reflection Across | Algebraic Rule | Example |
|---|---|---|
| x-axis | (x, y) reflects to (x, -y) | (2, 3) -> (2, -3) |
| y-axis | (x, y) reflects to (-x, y) | (2, 3) -> (-2, 3) |
| Origin | (x, y) reflects to (-x, -y) | (2, 3) -> (-2, -3) |
| Line y = x | (x, y) reflects to (y, x) | (2, 3) -> (3, 2) |
Explanation of Reflection Rules
- Reflection across the x-axis: The x-coordinate remains the same, while the y-coordinate changes its sign.
- Reflection across the y-axis: The y-coordinate remains the same, while the x-coordinate changes its sign.
- Reflection across the origin: Both the x and y coordinates change their signs. According to the reference, the rule of translation for each point is (a, b) reflects to (-a, -b).
- Reflection across the line y = x: The x and y coordinates are swapped. The reference indicates that the reflection of the point (a, b) across the line y = x is (b, a).
How to Apply Reflection Rules
By following these algebraic rules, you can reflect any point or figure across the x-axis, y-axis, origin, or the line y = x. These are the most common lines and points of reflection.
