Reflecting Objects Across The Y-Axis

🔑 Key Concepts

• A reflection across the \(y\)-axis flips a figure to the opposite side of the \(y\)-axis.
• The \(x\)-coordinate changes signs when reflecting across the \(y\)-axis.
• The \(y\)-coordinate stays the same.
• The reflection rule is \( (x,y)\rightarrow(-x,y) \).
• A reflection is a rigid transformation because the image keeps the same size and shape.

✏️ Worked Examples

Reflect Triangle \(ABC\) Across the \(y\)-Axis

Original coordinates:

\(A(3,-3)\), \(B(7,-3)\), \(C(3,-7)\)

Use the \(y\)-axis reflection rule:

\((x,y)\rightarrow(-x,y)\)

This means the \(x\)-values become opposites, while the \(y\)-values stay the same.

\(A(3,-3)\rightarrow A'(-3,-3)\)

\(B(7,-3)\rightarrow B'(-7,-3)\)

\(C(3,-7)\rightarrow C'(-3,-7)\)

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New coordinates:
\(A'=(-3,-3)\), \(B'=(-7,-3)\), \(C'=(-3,-7)\)

🧠 Math Vocabulary

• Reflection: a transformation that flips a figure across a line.
• Line of Reflection: the mirror line that the figure is reflected across.
• \(y\)-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.
• Corresponding Points: matching points on the preimage and image, such as \(A\) and \(A'\).
• Transformation: a movement or change of a figure on the coordinate plane.

💡 Main Idea

To reflect a figure across the \(y\)-axis, change each \(x\)-coordinate to its opposite and keep each \(y\)-coordinate the same. This flips the figure across the vertical axis without changing its size or shape.

📚 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 \(y\)-axis, students can practice reflections across the \(x\)-axis, vertical lines, horizontal lines, and compare reflections with translations, rotations, and dilations.

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