Reflecting A Triangle Across The Y-Axis

🔑 Key Concepts

• A reflection flips a figure across a line of reflection.
• When reflecting across the \(y\)-axis, the \(x\)-coordinate changes signs.
• The \(y\)-coordinate stays the same when reflecting across the \(y\)-axis.
• The rule for reflecting across the \(y\)-axis is \( (x,y)\rightarrow(-x,y) \).
• A reflection is a rigid transformation because the size and shape of the figure do not change.

✏️ Worked Examples

Visual Reference

Reflect Point \(A\)

Point \(A\) is located at:

\(A(-1,4)\)

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

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

Change the sign of the \(x\)-coordinate. Keep the \(y\)-coordinate the same.

\((-1,4)\rightarrow(1,4)\)

\(A'=(1,4)\)

Reflect Point \(B\)

Point \(B\) is located at:

\(B(4,-4)\)

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

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

The \(x\)-coordinate changes from positive to negative. The \(y\)-coordinate stays \(-4\).

\((4,-4)\rightarrow(-4,-4)\)

\(B'=(-4,-4)\)

Reflect Point \(C\)

Point \(C\) is located at:

\(C(-1,-6)\)

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

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

Change the \(x\)-coordinate from \(-1\) to \(1\). Keep the \(y\)-coordinate the same.

\((-1,-6)\rightarrow(1,-6)\)

\(C'=(1,-6)\)

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New coordinates:
\(A'=(1,4)\), \(B'=(-4,-4)\), \(C'=(1,-6)\)

🧠 Math Vocabulary

• Reflection: a transformation that flips a figure across a line.
• Line of Reflection: the mirror line that a figure is reflected across.
• Rigid Transformation: a transformation that preserves size and shape.
• Line of Symmetry: a line that divides a figure into two matching mirror-image parts.
• 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

Reflecting a figure across the \(y\)-axis flips the figure to the opposite side of the \(y\)-axis. The \(x\)-coordinates change signs, but the \(y\)-coordinates stay the same.

📚 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 understand positive and negative numbers on the coordinate plane.

🚀 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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