Key Concepts: Reflections

Definition

A reflection flips a figure over a line called the line of reflection. Each point and its image are the same distance from the line of reflection.

Coordinate Rules

• Reflection over the x-axis: (x, y) → (x, −y)
• Reflection over the y-axis: (x, y) → (−x, y)
• Reflection over y = x: (x, y) → (y, x)
• Reflection over y = −x: (x, y) → (−y, −x)

Properties of Reflections

• A reflection is an isometry (preserves distances and angle measures).
• The line of reflection is the perpendicular bisector of every segment connecting a point to its image.
• Orientation is reversed (the image is a mirror image).