Lecture Notes: Reflections over Axes

Definition of Reflection

• Reflection: A transformation in which a figure is flipped over a line of symmetry.
  • Example: A figure is flipped over the Y-axis; the line of symmetry is marked as yellow.
  • Each point and its image are equidistant from the line of reflection.

Example of Reflection

• Example using coordinates A, B, C:
  • A to A': Both are 3 units away from the line of symmetry.
  • B to B': Both are 1 unit away.
  • C to C': Both are 4 units away.

Reflection over the X-axis

• Pre-image Coordinates:
  • X: (-3, 1)
  • Y: (1, 4)
  • Z: (3, 2)
• Reflection Procedure:
  • Flip across the X-axis (horizontal line).
  • X's coordinates change to X': (-3, -1)
  • Y's coordinates change to Y': (1, -4)
  • Z's coordinates change to Z': (3, -2)
• Rule for Reflection over X-axis:
  • X-coordinate remains the same.
  • Y-coordinate becomes negative.

Reflection Rule Example

• Using points D, E, F:
  • D: (-3, -3) to D': (-3, 3) (Y becomes positive)
  • E: (3, -2) to E': (3, 2) (Y becomes positive)
  • F: (2, 0) to F': (2, 0) (No change for Y=0)

Reflection over the Y-axis

• Pre-image Coordinates:
  • P: (-4, -3)
  • Q: (-3, 3)
  • R: (-1, 2)
• Reflection Procedure:
  • Flip across the Y-axis (vertical line).
  • P's coordinates change to P': (4, -3)
  • Q's coordinates change to Q': (3, 3)
  • R's coordinates change to R': (1, 2)
• Rule for Reflection over Y-axis:
  • Y-coordinate remains the same.
  • X-coordinate becomes negative.

Reflection Rule Application

• Using points L, M, N:
  • L: (-2, 4) to L': (2, 4) (X becomes positive)
  • M: (2, 1) to M': (-2, 1)
  • N: (-4, -3) to N': (4, -3)

Summary

• Two methods for reflecting points:
  • Counting squares on a graph.
  • Applying transformation rules to coordinates.
• Reflection over X-axis: X remains unchanged, Y becomes negative.
• Reflection over Y-axis: Y remains unchanged, X becomes negative.