📚 Topic Summary
Reflecting a point over the x-axis is like creating a mirror image of that point, with the x-axis acting as the mirror. The x-coordinate stays the same, but the y-coordinate changes its sign. If the original point is $(x, y)$, the reflected point will be $(x, -y)$. For example, reflecting the point (2, 3) over the x-axis gives you (2, -3). Think of it as flipping the point vertically!
Let's say you have a shape and you want to reflect the whole shape over the x-axis. You just need to reflect each point of the shape over the x-axis, and then connect the reflected points together.
🔤 Part A: Vocabulary
Match the terms with their definitions:
- Term: Reflection
- Term: X-axis
- Term: Coordinate
- Term: Origin
- Term: Image
- Definition: The horizontal line on a coordinate plane.
- Definition: The new point or shape after a transformation.
- Definition: A transformation that creates a mirror image.
- Definition: The point (0,0) on a coordinate plane.
- Definition: A number that identifies a point's position.
✍️ Part B: Fill in the Blanks
When reflecting a point over the x-axis, the ______ coordinate stays the same, but the ______ coordinate changes its ______. For example, the reflection of (4, -2) over the x-axis is (4, ______).
🤔 Part C: Critical Thinking
Imagine you have a triangle ABC with coordinates A(1, 2), B(3, 4), and C(5, 1). After reflecting this triangle over the x-axis, what are the new coordinates of triangle A'B'C'? Explain how you found your answer.