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Mastering Geometry Reflections: Definitions, Examples & Practice

Learn about reflections in geometry with definitions, examples, and practice exercises. Understand how to plot points and lines through reflection over various axes or lines. Engage in reflective learning to enhance your geometry skills.

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Mastering Geometry Reflections: Definitions, Examples & Practice

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  1. y 10 x -10 10 -10 Review: Graph y = -4

  2. Reflections Geometry Unit 8, Day 2 Ms. Reed

  3. What is a Reflection? • Definition: A flip. • Example?

  4. How to do a Reflection • Plot the point(s). • Count from the point to the line of reflection. • Count the same number of spaces in the opposite direction. • Plot the image.

  5. y 10 x -10 10 A” A -10 A’ Graphing Coordinates • Plot the point A(4,6). • Reflect the point (4,6) over the x-axis. Label this point A’ and state the coordinates. • Reflect the point (4,6) over the y-axis. Label this point A” and state the coordinates. (4,-6) (-4,6)

  6. y 10 x -10 10 -10 Refresh Your Memory: Horizontal and Vertical Lines • Graph the following lines: • Y=5 • Y=-2 • X=4 • X=-6 Y=5 X=-6 X=4 Y=-2

  7. y 10 x -10 10 A” A -10 A’ Graphing Coordinates • Plot the point A(4,6). • Reflect the point (4,6) over the line x=-1. Label this point A’. • Reflect the point (4,6) over the line y=2. Label this point A”. y=2 (-6,6) x=-1 (4,-2)

  8. y 10 x -10 10 -10 More Reflection Examples • Graph the vertices of parallelogram WXYZ. • W(-3,5) • X(1,5) • Y(2,3) • Z(-2,3) • Reflect the parallelogram over the x-axis. W X • W’(-3,-5) • X’(1,-5) • Y’(2,-3) • Z’(-2,-3) Z Y Z’ Y’ W’ X’

  9. y 10 x -10 10 -10 More Reflection Examples • Graph the vertices of parallelogram WXYZ. • W(-3,1) • X(1,1) • Y(2,-1) • Z(-2,-1) • Reflect the parallelogram over the line x=-2 • W’(-1,1) • X’(-5,1) • Y’(-6,-1) • Z’(-2,-1) X’ W’ W X Z Y Y’ Z’ x=-2

  10. Practice with Line Reflections • http://www.regentsprep.org/Regents/math/geometry/GT1/Prac1.htm

  11. More Practice: • The image of the point (4,-3) under a reflection across the x-axis is… • (4,3) • The image of the point (-5,4) under a reflection across the y-axis is… • (5,4)

  12. Think about it: • The image of the point (-1, 8) under a reflection across the line y = x is … • (8, -1)

  13. Homework Work Packet: Reflections

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