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12-4

Graphing Reflections. 12-4. Course 1. Warm Up. Problem of the Day. Lesson Presentation. Graphing Reflections. 12-4. Course 1. Warm Up A parallelogram has vertices (-4, 1), (0, 1), (-3, 4), and (1, 4). What are its vertices after it has been translated 4 units right and 3 units up?.

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12-4

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  1. Graphing Reflections 12-4 Course 1 Warm Up Problem of the Day Lesson Presentation

  2. Graphing Reflections 12-4 Course 1 Warm Up A parallelogram has vertices (-4, 1), (0, 1), (-3, 4), and (1, 4). What are its vertices after it has been translated 4 units right and 3 units up? (0, 4), (4, 4), (1, 7), (5, 7)

  3. Graphing Reflections 12-4 Course 1 Problem of the Day These are rits: 24042, 383, and 4994. These are not rits: 39239, 28, and 5505. Which of these are rits: 39883, 4040, and 101? Why? 101 is a rit because it is the same forward and backward.

  4. Graphing Reflections 12-4 Course 1 Learn to use reflections to change the positions of figures on a coordinate plane.

  5. Graphing Reflections 12-4 y 8 6 4 2 x -8 -6 -4 -2 2 4 6 8 -2 -4 -6 -8 Course 1 Additional Example 1: Reflecting Figures on a Coordinate Plane Give the coordinates of the figure after the given reflection. Reflect parallelogram EFGH across the y-axis. E F H G

  6. Graphing Reflections 12-4 To reflect the parallelogram across the y-axis, write the opposites of the x-coordinates. The y-coordinates do not change. Course 1 Additional Example 1 Continued EFGH E’F’G’H’ E(–4, 0) E’(4, 0) F(0, 0) F’(0, 0) G(–2, –3) G’(2, –3) H(–6, –3) H’(6, –3)

  7. Graphing Reflections 12-4 y 8 6 4 2 x F’ E’ -8 -6 -4 -2 2 4 6 8 -2 -4 H’ G’ -6 -8 Course 1 Additional Example 1 Continued Reflect parallelogram EFGH across the y-axis. F E H G

  8. Graphing Reflections 12-4 y 8 6 4 2 x -8 -6 -4 -2 2 4 6 8 -2 -4 -6 -8 Course 1 Try This: Example 1 Give the coordinates of the figure after the given reflection. Reflect parallelogram EFGH across the x-axis. E F H G

  9. Graphing Reflections 12-4 To reflect the parallelogram across the x-axis, write the opposites of the y-coordinates. The x-coordinates do not change. Course 1 Try This: Example 1 Continued EFGH E’F’G’H’ E(–4, 0) E’(–4, 0) F(0, 0) F’(0, 0) G(–2, –3) G’(–2, 3) H(–6, –3) H’(–6, 3)

  10. Graphing Reflections 12-4 y 8 G’ H’ 6 F’ 4 E’ 2 x -8 -6 -4 -2 2 4 6 8 -2 -4 -6 -8 Course 1 Try This: Example 1 Continued Reflect parallelogram EFGH across the x-axis. F E H G

  11. Graphing Reflections 12-4 y 8 6 4 2 x -8 -6 -4 -2 2 4 6 8 -2 -4 -6 -8 Course 1 Additional Example 2: Design ApplicationA designer is using a stencil that is shaped like the figure below. A pattern is made by reflecting the figure across the x-axis. Give the coordinates of the vertices of the figure after the reflection. P S Q R

  12. Graphing Reflections 12-4 To reflect the quadrilateral across the x-axis, write the opposites of the y-coordinates. The x-coordinates do not change. Course 1 Additional Example 2 Continued PQRS P’Q’R’S’ P(1, 7) P’(1, –7) Q(2, 1) Q’(2, –1) R(–1, 1) R’(–1, –1) S(–3, 3) S’(–3, –3)

  13. Graphing Reflections 12-4 y 8 6 4 R’ Q’ 2 x S’ -8 -6 -4 -2 2 4 6 8 -2 P’ -4 -6 -8 Course 1 Additional Example 2 Continued P S Q R

  14. Graphing Reflections 12-4 y 8 6 4 2 x -8 -6 -4 -2 2 4 6 8 -2 -4 -6 -8 Course 1 Try This: Example 2 A designer is using a stencil that is shaped like the figure below. A pattern is made by reflecting the figure across the y-axis. Give the coordinates of the vertices of the figure after the reflection. P S Q R

  15. Graphing Reflections 12-4 To reflect the quadrilateral across the y-axis, write the opposites of the x-coordinates. The y-coordinates do not change. Course 1 Try This: Example 2 Continued PQRS P’Q’R’S’ P(–3, 7) P’(3, 7) Q(–2, 1) Q’(2, 1) R(–5, 1) R’(5, 1) S(–7, 3) S’(7, 3)

  16. Graphing Reflections 12-4 P’ y S’ 8 Q’ R’ 6 4 2 x -8 -6 -4 -2 2 4 6 8 -2 -4 -6 -8 Course 1 Try This: Example 2 Continued P S Q R

  17. Graphing Reflections 12-4 Course 1 Insert Lesson Title Here Lesson Quiz Give the coordinates of the vertices of each figure after the given reflection. 1. Reflect triangle ABC with vertices A(5, 1), B(2, 3), and C(4, 6) across the x-axis. 2. Reflect parallelogram PQRS with vertices P(–4, –4), Q(1, –4), R(–2, 2), and S(3, 2) across the y-axis. A’(5, –1), B’(2, –3), C’(4, –6) P’(4, –4), Q’(–1, –4), R’(2, 2), and S’(–3, 2)

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