Coordinate Rules: Reflection Across the X-Axis and Y-Axis
Grade 7 students in Big Ideas Math Advanced 2 (Chapter 2: Transformations) master coordinate rules for reflecting points across the x-axis and y-axis. The rule for x-axis reflection is (x, y) to (x, -y), and for y-axis reflection is (x, y) to (-x, y)—the axis you reflect across stays the same.
Key Concepts
Property When reflecting across the main coordinate axes, we use simple algebraic rules instead of counting. Across the X Axis: The rule is $(x, y) \rightarrow (x, y)$. The x coordinate stays exactly the same, and the y coordinate changes to its opposite sign. Across the Y Axis: The rule is $(x, y) \rightarrow ( x, y)$. The y coordinate stays exactly the same, and the x coordinate changes to its opposite sign. Memory Trick: "The axis you reflect across is the letter that stays the same!".
Examples Reflect across X axis (y changes): Point (3, 4) becomes (3, 4). Point ( 2, 5) becomes ( 2, 5). Reflect across Y axis (x changes): Point (3, 2) becomes ( 3, 2). Point ( 4, 1) becomes (4, 1). Points ON the mirror: Reflect (0, 5) across the Y axis. Since the rule says change the sign of x, 0 is still 0. The point stays at (0, 5) because it is already touching the mirror!
Explanation Why does this math work? Imagine jumping over the horizontal x axis. You are moving Up or Down. "Up and Down" is the y direction! That is why the y value flips (positive becomes negative, or negative becomes positive), while your left/right position (x) doesn't change at all. Always double check your signs: changing a sign means if it was already negative, it becomes positive.
Common Questions
What is the coordinate rule for reflecting across the x-axis?
The rule is (x, y) to (x, -y). The x-coordinate stays the same, and the y-coordinate changes sign. For example, (3, 4) reflects to (3, -4).
What is the coordinate rule for reflecting across the y-axis?
The rule is (x, y) to (-x, y). The y-coordinate stays the same, and the x-coordinate changes sign. For example, (3, 2) reflects to (-3, 2).
How do you remember reflection coordinate rules?
Use this memory trick: the axis you reflect across is the letter that stays the same! Reflecting across the x-axis keeps x the same; reflecting across the y-axis keeps y the same.
What chapter in Big Ideas Math Advanced 2 covers reflection coordinate rules?
Chapter 2: Transformations in Big Ideas Math Advanced 2 (Grade 7) covers coordinate rules for reflections across the x-axis and y-axis.
What happens to a point on the axis of reflection?
A point that lies on the line of reflection does not move. For example, reflecting (0, 5) across the y-axis gives (0, 5) because it is already on the y-axis.