📚 Practice With Worksheets
Extend your learning by practicing reflections across the x-axis and y-axis and analyzing how coordinates change under reflection transformations.
▶️ Learn With Videos
Watch these lessons to learn how reflections change coordinates when figures are reflected across the x-axis and y-axis.
🛠️ How to Use This Tool
Use the Reflection Explorer to investigate how a figure changes when it is reflected across a line on the coordinate plane.
Drag the vertices of triangle \(ABC\), choose a vertical or horizontal line of reflection, and use the slider to move the line from \(-10\) to \(10\).
Click Reflect Across Line to create the reflected image. The original figure remains as a shadow so you can compare the preimage and image.
🧠 Things to Think About
How are the coordinates of a point changed when it is reflected across the \(x\)-axis or the \(y\)-axis?
What stays the same after a reflection? What changes?
How does the line of reflection act like a mirror between a point and its reflected image?
📘 Vocabulary
Transformation: A change in the position, size, or orientation of a figure.
Reflection: A transformation that flips a figure across a line.
Line of Reflection: The line that acts like a mirror during a reflection.
Preimage: The original figure before a transformation.
Image: The new figure after a transformation.
Prime Notation: A way to label transformed points. For example, \(A'\) is read as “A prime.”
Rigid Transformation: A transformation that preserves size and shape.
Congruent: Figures that have the same size and shape.
Coordinate Rule: A rule that describes how the coordinates of a point change during a transformation.
📐 Reflection Rules
Reflecting across the \(x\)-axis changes the sign of the \(y\)-coordinate:
\((x,y) \rightarrow (x,-y)\)
Reflecting across the \(y\)-axis changes the sign of the \(x\)-coordinate:
\((x,y) \rightarrow (-x,y)\)
For a vertical line \(x=k\), the \(y\)-coordinate stays the same and the new \(x\)-coordinate is the same distance on the other side of the line. For a horizontal line \(y=k\), the \(x\)-coordinate stays the same and the new \(y\)-coordinate is the same distance on the other side of the line.
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