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Translations

Translations. Lesson 9-8. Translations. Translations are used on the coordinate plane. A translation is a shift or movement of a figure a given number of places on the coordinate plane. EXAMPLE. Suppose we have parallelogram ABCD as shown on the graph. We can “translate” this shape

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Translations

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  1. Translations Lesson 9-8

  2. Translations • Translations are used on the coordinate plane. • A translation is a shift or movement of a figure a given number of places on the coordinate plane.

  3. EXAMPLE Suppose we have parallelogram ABCD as shown on the graph. We can “translate” this shape 5 units to the right and 3 units down. The new image would look like this: A B C D

  4. Notice that the entire new image Is shifted 5 units to the right and 3 units down. The labels of the image are noted with a prime ‘ symbol. A B A’ B’ C D C’ D’

  5. TRY THIS Translate triangle QRS 4 units to The left and 5 units up. Q R S

  6. TRY THIS Q’ Translate triangle QRS 4 units to The left and 5 units up. R’ Q S’ R S

  7. Symmetry and Reflections Lesson 9-9

  8. Reflection is a mirror image of a figure. • In geometry, reflectional symmetry occurs when one half of a figure is a mirror image of the other half. • The line of symmetry is the line that divides a figure into two congruent halves.

  9. Symmetry • Notice that one half of the pentagon is the mirror image of the other. Line of symmetry

  10. Try This • Which of the following figures have reflectional symmetry?

  11. Try This • Which of the following figures have reflectional symmetry? YES NO YES YES YES

  12. Symmetry • Many figures have more than one line of symmetry. Notice that the square has 4 lines of symmetry.

  13. Try This • Draw all the lines of symmetry for the following figures.

  14. Try This • Draw all the lines of symmetry for the following figures.

  15. Try This • Draw all the lines of symmetry for the following figures.

  16. Try This • Draw all the lines of symmetry for the following figures.

  17. Try This • Draw all the lines of symmetry for the following figures.

  18. Try This • Draw all the lines of symmetry for the following figures.

  19. Reflections • Reflections can also be used on the coordinate plane. • A reflection is a figure that has been flipped over a line of reflection.

  20. EXAMPLE Suppose that line segment AB is graphed as shown. If it is reflected over the y-axis, it would look like this: A B

  21. EXAMPLE Notice that the image of the line segment is a mirror image of the original one. It is as if the paper were folded on the y-axis and it left an identical imprint on the other side of the axis. A A’ B B’

  22. Try This Graph the image of triangle DEF after a reflection over the x-axis. D E F

  23. Try This D E F F’ E’ D’

  24. Try This Now graph the image of parallelogram ABCD after it is reflected over x = 2 A B C D

  25. Try This Line of reflection A B B’ A’ C D D’ C’ Notice that the line of reflection is x = 2. It is as if the paper were folded on the line x = 2.

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