📝 Practice Worksheets
🛠️ Related Tools
🔑 Key Concepts
- A reflection flips a figure across a line of reflection.
- Reflecting across the \(x\)-axis changes the sign of the \(y\)-coordinate.
- Reflecting across the \(y\)-axis changes the sign of the \(x\)-coordinate.
- Reflections preserve side lengths and angle measures.
- A reflection is a rigid transformation because the image keeps the same size and shape as the preimage.
✏️ 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 ordered pairs change during a transformation.
- Corresponding Points: matching points on the preimage and image, such as \(A\) and \(A'\).
💡 Main Idea
Reflections across the coordinate axes can be found quickly using coordinate rules. Across the \(x\)-axis, keep \(x\) the same and change \(y\) to its opposite. Across the \(y\)-axis, change \(x\) to its opposite and keep \(y\) the same.
📚 What You Should Already Know
Students should know how to plot ordered pairs, identify the \(x\)-axis and \(y\)-axis, read points from a coordinate plane, and find opposites of positive and negative numbers.
🚀 What Comes Next
After practicing reflections across the coordinate axes, students can reflect figures across horizontal and vertical lines such as \(y=4\) or \(x=-2\), and compare reflections with translations, rotations, and dilations.
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