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Reflection Transformations: Analyzing Flipping Shapes Across Axes

Explore the concept of reflection in geometry, focusing on how a shape can be flipped across a line, resulting in a mirror image. Learn about congruency and orientation differences between the original shape and its reflection, using the example of polygon ABCD and its reflected counterpart ABCD'. Analyze the coordinates of points on the shape before and after reflection across the x and y axes, and discover patterns in their values. Enhance your understanding of geometric transformations through these insightful reflections.

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Reflection Transformations: Analyzing Flipping Shapes Across Axes

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  1. The Leaner Twins Lefty Righty

  2. Graphing Transformations 2 Reflection - flipping a shape across a line so it faces the opposite direction.

  3. y 4 figure image B’ B 3 C C’ 2 1 A’ A x D D’ -4 -3 -2 -1 1 2 3 4 -1 -2 -3 -4 A reflection of ABCD in the y-axis

  4. y 4 B 3 2 C 1 A x D -4 -3 -2 -1 1 2 3 4 D’ A’ -1 -2 C’ -3 B’ -4 A reflection of ABCD in the x-axis A reflection of ABC in the y-axis

  5. y mirror line 4 B 3 2 C 1 A x D C’ -4 -3 -2 -1 1 2 3 4 D’ -1 -2 B’ -3 A’ -4 A reflection of ABCD across a mirror line

  6. How are a figure and its reflection image alike? They are congruent.

  7. How are a figure and its reflection image different? They have different orientations. If ABCD is read clockwise, A’B’C’D’ is read counter-clockwise.

  8. How do you identify a reflection? Check that corresponding points are the same distance from the mirror line.

  9. y Coordinates 4 B’ B 3 A(-4,1) B(-2,3) C(0,2) D(-1,0) C C’ 2 1 A’ A x D D’ -4 -3 -2 -1 1 2 3 4 A’(4,1) B’(2,3) C’(0,2) D’(1,0) -1 -2 -3 -4 A reflection of ABCD in the y-axis

  10. What patterns do you see in the coordinates of the figure and its image? • y-coordinates are the same because the shape does not go up or down • x-coordinates are the opposite because the shape was reflected in the y-axis

  11. y Coordinates 4 B 3 A(-4,1) B(-2,3) C(0,2) D(-1,0) 2 C 1 A x D -4 -3 -2 -1 1 2 3 4 D’ A’ -1 A’(-4,-1) B’(-2,-3) C’(0,-2) D’(-1,0) -2 C’ -3 B’ -4 A reflection of ABCD in the x-axis A reflection of ABC in the y-axis

  12. What patterns do you see in the coordinates of the figure and its image? • x-coordinates are the same because the shape does not go left or right • y-coordinates are the opposite because the shape was reflected in the x-axis

  13. y Coordinates 4 B 3 A(-4,1) B(-2,3) C(0,2) D(-1,0) 2 C 1 A x D C’ -4 -3 -2 -1 1 2 3 4 D’ -1 A’(1,-4) B’(3,-2) C’(2,0) D’(0,-1) -2 B’ -3 A’ -4 A reflection of ABCD across a mirror line

  14. What pattern do you see in the coordinates of the figure and its image? • x-coordinates and y-coordinates switch places

  15. y 4 A 3 B D 2 1 x -4 -3 -2 -1 1 2 3 4 C -1 -2 -3 -4 Reflect ABCD across the y-axis and x-axis.

  16. y 4 A 3 B D 2 1 x -4 -3 -2 -1 1 2 3 4 C -1 -2 -3 -4 Reflect ABCD across the mirror line.

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