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Reflections on the Coordinate Plane

Reflections on the Coordinate Plane. Reflections on the Coordinate Plane. The undisturbed surface of a pond acts like a mirror and can provide the subject for beautiful photographs. Reflections on the Coordinate Plane.

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Reflections on the Coordinate Plane

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  1. Reflections on the Coordinate Plane

  2. Reflections on the Coordinate Plane • The undisturbed surface of a pond acts like a mirror and can provide the subject for beautiful photographs

  3. Reflections on the Coordinate Plane • We call the waterline a “line of symmetry” because if the photo were folded at the waterline, the two halves would form a mirror image of each other

  4. Reflections on the Coordinate Plane • Similarly, the x or y-axis can act as a line of symmetry on the coordinate plane.

  5. Reflections Mini-Lab • Count how many units point A is from the x-axis. Then count that many units on the opposite side of the x-axis and label this point A’ C A B 3 units 3 units A’

  6. Reflections Mini-Lab • Count how many units point B is from the x-axis. Then count that many units on the opposite side of the x-axis and label this point B’ C A B 1 unit 1 unit B’ A’

  7. Reflections Mini-Lab • Count how many units point C is from the x-axis. Then count that many units on the opposite side of the x-axis and label this point C’ C A B 5 units B’ 5 units A’ C’

  8. Reflections Mini-Lab • Draw triangle A’B’C’ • What do you notice about the two triangles? Triangle A’B’C’ is a reflection of triangle ABC C A B B’ A’ C’

  9. Reflections Mini-Lab • Compare the coordinates of A with A’, B with B’, and C with C’ • What pattern do you notice? C A B A (1, 3) B (5, 1) C (3, 5) A’ (1, -3) B’ (5, -1) C’ (3, -5) B’ Same x value, Opposite y value A’ C’

  10. Reflections Mini-Lab • The reflection in this mini-lab is a reflection over the x-axis. • The x-axis acts as the line of symmetry C A B A (1, 3) B (5, 1) C (3, 5) A’ (1, -3) B’ (5, -1) C’ (3, -5) B’ A’ C’

  11. Reflections Mini-Lab • To reflect a figure over the x-axis, use the same x-coordinate and multiply the y-coordinate by -1 C A B A (1, 3) B (5, 1) C (3, 5) A’ (1, -3) B’ (5, -1) C’ (3, -5) B’ A’ C’

  12. Reflections Mini-Lab • What do you think would happen if we multiplied the original x-coordinate by -1 and used the same y-coordinate? C’ C A B A (1, 3) B (5, 1) C (3, 5) A’ (-1, 3) B’ (-5, 1) C’ (-3, 5) A’ B’ You create a reflection over the y-axis!

  13. Reflections Mini-Lab What did we learn? • To reflect a figure over the x-axis, use the same x-coordinate and multiply the y-coordinate by -1 • To reflect a figure over the y-axis, multiply the x-coordinate by -1 and use the same y-coordinate

  14. Reflections on the Coordinate Plane Checkpoint • If square MATH is reflected into quadrant II, what is the line of symmetry? The y-axis M A H T

  15. Reflections on the Coordinate Plane Checkpoint • What are the coordinates of square MATH when reflected over the y-axis? M’ (-1, 4) M A H T A’ (- 4, 4) T’ (-4, 1) H’ (- 1, 1)

  16. Reflections on the Coordinate Plane Checkpoint • If square MATH is reflected into quadrant IV, what is the line of symmetry? The x-axis M A H T

  17. Reflections on the Coordinate Plane Checkpoint • What are the coordinates of square MATH when reflected over the x-axis? M’ (1,- 4) M A H T A’ (4,- 4) T’ (4,- 1) H’ (1,- 1)

  18. Homework • Practice Worksheet 11-9 • Practice Skills 6-7 • Due Tomorrow!!

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