Lecture Notes: Translation and Reflection in Coordinate Geometry

Introduction

• Focus on performing geometric transformations:
  • Translation
  • Reflection
• Using coordinate plane transformations on points

Translation

• Objective: Translate points four units right and one unit down.
• Translate each point individually:
  • Point F:
    • Original location not specified explicitly.
    • Move 4 units right.
    • Move 1 unit down.
    • New position: F' (details described further)
  • Point G:
    • Original location not specified explicitly.
    • Move 4 units right.
    • Move 1 unit down.
    • New position: G' (details described further)
  • Point Y:
    • Original location not specified explicitly.
    • Move 4 units right.
    • Move 1 unit down.
    • New position: Y' (details described further)

New Coordinates After Translation

• F':
  • Starting from the origin: move left 1, up 3
  • Coordinates: (-1, 3)
• G':
  • Starting from the origin: move none left/right, down 1
  • Coordinates: (0, -1)
• Y':
  • Starting from the origin: move left 1, no movement up/down
  • Coordinates: (-1, 0)

Reflection Across the X-axis

• Objective: Reflect translated points across the x-axis.
• Reflection Concept:
  • Draw a mirror line on the x-axis.
  • For each point, measure and mark the equivalent distance on the opposite side of the axis.

New Coordinates After Reflection

• G'':
  • G' was 1 unit away from the x-axis.
  • Reflect to place 1 unit on the opposite side.
  • Coordinates remain (0, -1) due to reflection symmetry.
• F'':
  • F' was 3 units away from the x-axis.
  • Reflect to place 3 units on the opposite side.
  • Coordinates: (-1, -3)
• Y'':
  • Y' was on the mirror line.
  • Y'' remains unchanged.
  • Coordinates: (-1, 0)

Observations

• When reflecting across an axis, the y-coordinate changes sign.
• Transformation sequence demonstrates two operations in one coordinate plane.
• Important for visualizing and understanding geometry transformations.

Conclusion

• This exercise shows practical application of translation and reflection on points in a coordinate plane.
• Understanding these basics is crucial for more complex geometric transformations.