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Understanding Reflection in Geometry: Transformations Across Axes

This lesson explores the concept of reflection in geometry, focusing on transformations across the x-axis and y-axis. Students will learn how to reflect points across these axes using specific rules, such as how the coordinates change during reflection. The lesson includes examples illustrating these concepts, an examination of lines of symmetry, and isometries that preserve angles and distances. Students will solve various problems from the textbook to solidify their understanding.

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Understanding Reflection in Geometry: Transformations Across Axes

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  1. Week 1 Warm Up 01.04.12

  2. Line of Reflection The mirror in the transformation. Ex 1

  3. Reflection on a plane: x-axis • • Ex 2 • • -2 2

  4. Reflection on a plane: x-axis B( 3, 4 ) • • • • Ex 2 • • A( 2, 2 ) 4 • • A’( 2, -2 ) -4 B’( 3, -4 ) Rule 1 If ( x, y ) reflects across the x-axis its image is ( x, -y ).

  5. Reflection on a plane: y-axis Ex 3 A’( -3, 2 ) A( 3, 2 ) If ( x, y ) reflects across the y-axis its image is ( -x, y ). Rule 2

  6. If a figure can be mapped onto itself by reflection. Lines of Symmetry Ex 4

  7. Theorem 7.1 Isometry A transformation that preserves angles and distances. Ex 5 Ex 6

  8. Do 1 : AB ? Do 2 : Do 3 : Do 4 : ∠DEF ? ∠GFE ? DG ? Assignment: Textbook page 407, 15 - 29 All.

  9. Line of Reflection The mirror in the transformation. Ex 1

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