📝 Practice Worksheets
🛠️ Related Tools
🔑 Key Concepts
- A reflection across the \(x\)-axis flips a figure above or below the \(x\)-axis.
- When reflecting across the \(x\)-axis, the \(x\)-coordinate stays the same.
- The \(y\)-coordinate changes to its opposite when reflecting across the \(x\)-axis.
- The reflection rule for the \(x\)-axis is \( (x,y)\rightarrow(x,-y) \).
- A reflection is a rigid transformation because the image keeps the same size and shape.
✏️ Worked Examples
🧠 Math Vocabulary
- Reflection: a transformation that flips a figure across a line.
- Line of Reflection: the mirror line that the figure is reflected across.
- \(x\)-axis: the horizontal axis on the coordinate plane, where \(y=0\).
- \(y\)-axis: the vertical axis on the coordinate plane, where \(x=0\).
- Rigid Transformation: a transformation that preserves size and shape.
- Image: the new figure after a transformation.
- Preimage: the original figure before a transformation.
- Coordinate Rule: an algebraic rule that shows how each ordered pair changes during a transformation.
- Corresponding Points: matching points on the preimage and image, such as \(A\) and \(A'\).
💡 Main Idea
To reflect across the \(x\)-axis, keep the \(x\)-coordinate the same and change the sign of the \(y\)-coordinate. Reflections are rigid transformations, so the image keeps the same size and shape as the preimage.
📚 What You Should Already Know
Students should know how to plot ordered pairs, identify the \(x\)-axis and \(y\)-axis, read coordinates from a graph, and find opposites of positive and negative numbers.
🚀 What Comes Next
After reflecting across the \(x\)-axis, students can practice reflections across the \(y\)-axis, horizontal lines, vertical lines, and compare reflections with translations, rotations, and dilations.
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