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Understanding Reflections and Transformations in Geometry

This resource explores the concept of reflections in geometry, providing a series of examples for reflecting triangles, rectangles, and trapeziums across various mirror lines, such as the x-axis, y-axis, and specific lines like x=1. Users will gain insights on how to obtain images of shapes after transformations, alongside coordinates for specific triangle vertices. The systematic approach illustrates the method for reflecting shapes across given lines in a coordinate plane, enhancing comprehension of transformations in geometry.

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Understanding Reflections and Transformations in Geometry

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  1. Transformations Reflections

  2. Mirror line Example Reflect ABCD in the given mirror line A D C B

  3. Example Reflect triangle PQR in the given mirror line Q R P Mirror line

  4. Example Reflect triangle LMN in the given mirror line Mirror line L M M

  5. Example Reflect the rectangle in the given mirror line Mirror line

  6. Example Reflect the trapezium in the given mirror line Mirror line

  7. y 4 3 2 1 0 x –5 –4 –3 –2 –1 1 2 3 4 5 –1 –2 –3 –4 –5 Example Reflect triangle ABC in the x axis A C B

  8. y 4 3 2 1 0 x –5 –4 –3 –2 –1 1 2 3 4 5 –1 –2 –3 –4 –5 Example Reflect triangle DEF in the y axis E F D

  9. y 4 3 2 1 0 x –5 –4 –3 –2 –1 1 2 3 4 5 –1 –2 –3 –4 –5 Example Reflect triangle GHK in the line x = 1 H K G

  10. y 4 3 2 1 0 x –5 –4 –3 –2 –1 1 2 3 4 5 –1 –2 –3 –4 –5 Example Reflect triangle LMN in the line N M L

  11. y 4 3 2 1 0 x –5 –4 –3 –2 –1 1 2 3 4 5 –1 –2 –3 –4 –5 Example Reflect triangle PQR in the line Q P R

  12. Example • Given ABC with A(1, 3) B(1, 5) and C(4, 5), obtain the image under the following transformations in each case. • Reflection in • Reflection in • Reflection in • Reflection in

  13. y 4 3 2 1 0 x –5 –4 –3 –2 –1 1 2 3 4 5 –1 –2 –3 –4 –5 • Example • Given ABC with A(1, 3) B(1, 5) and C(4, 5), obtain the image under the following transformations in each case. • Reflection in • Reflection in • Reflection in • Reflection in . C B A

  14. Example Complete the object below so that it has the given two lines of symmetry.

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