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x- and y-Axis Reflection Practice Game

x- and y-Axis Reflection Practice Game
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2021-01-18 21:24
SequenceCoordinate GeometryTransformationGeometric ConstructionGraphing
This example demonstrates a reflection practice game that randomly generates points/segments and asks learners to reflect the figure across the x-axis and y-axis, then compare the result. The key math concepts are geometric reflection (axis symmetry), congruence, and the coordinate-geometry correspondence between original and reflected points, including the fact that segment length is preserved under reflection. Construction and implementation highlights: RandomElement selects items randomly; Sequence and Flatten build candidate lists; Shuffle and Take randomize and pick subsets; Point and Segment create the original geometric objects; If is used for conditional logic (e.g., generating/choosing reflected objects and updating the outcome). The scene also includes interactive/interface objects such as button1, score, level, and text3/text4/text5 to support progression and scoring. Suitable for middle-school geometry/coordinate geometry lessons, practice sessions, and teaching transformation skills.

GeoGebra Commands & Parameters

  1. RandomElement(listRA) → refax, "j"
  2. Sequence(Sequence[(i, j), i, -10, 10], j, -10, 10) → listT
  3. Flatten(listT) → listR
  4. Shuffle(listR) → listS, {(-10, 2), (-1, 9), (-10, 1), (-2, -1), (-9, -5), (4, -3), (-2, -7), (9, 1), (9, -6), (4, -10), (-2, -3), (-5, -6), (-7, -9), (0, 3), (-7, 3), (9, 5), (10, -6), (6, 7), (6, -5), (-8, 3), (1, 4), (-1, 8), (10, 5), (10, 1), (8, -7), (-9, -9), (2, 4), (1, -4), (-1, -8), (-3, -5), (-6, -3), (0, -6), (-3, 4), (7, 2), (-1, -9), (-5, 1), (3, -7), (-3, -1), (-4, -2), (1, 1), (-4, -6), (-4, -3), (9, 7), (9, -8), (-3, 8), (3, 3), (6, -3), (-6, -8), (10, 0), (3, 9), (-9, -6), (-6, 6), (-7, -10), (9, -7), (-3, -8), (9, -9), (2, 3), (8, 10), (-10, -8), (0, 2), (3, 2), (8, 8), (-7, -5), (-1, 3), (3, -6), (-9, -2), (-8, -2), (6, -2), (-6, 3), (10, -10), (-1, 0), (-1, -6), (-5, -7), (2, 6), (-10, 3), (-4, 4), (-7, 0), (-6, 5), (5, 2), (-1, -7), (-5, 2), (-8, 1), (7, -5), (3, 4), (8, -9), (8, 4), (7, -1), (2, 0), (3, -1), (-5, 10), (8, -5), (-9, -3), (10, -4), (10, -1), (-2, 2), (-5, -2), (-3, 5), (0, 5), (5, 8), (-1, 10), (9, -4), (-4, 9), (0, -3), (6, -6), (-7, -1), (6, 10), (1, 6), (3, -9), (9, -10), (5, -4), (-8, -1), (-7, -6), (-10, 4), (4, 3), (1, -2), (-8, -7), (6, 9), (5, -1), (8, -4), (9, -2), (2, 2), (6, -4), (-4, -4), (-8, 8), (-1, -2), (-9, 1), (2, 10), (1, -5), (6, 1), (-7, 2), (10, 7), (-6, -6), (0, 7), (5, -9), (10, 9), (-5, 5), (-7, 9), (-10, -9), (8, -2), (-4, 5), (-5, -5), (10, 4), (4, -2), (-10, -4), (4, 1), (-9, 3), (4, -5), (-4, -8), (-3, 3), (-6, -7), (-3, -6), (0, -2), (4, 10), (7, 7), (-3, 1), (-6, 9), (0, -1), (9, 0), (6, 4), (10, 8), (0, -10), (5, -5), (8, 6), (5, -6), (6, 2), (-6, 1), (-1, 4), (6, -7), (-1, 2), (-8, 0), (-8, 4), (5, 7), (-6, 10), (-8, -5), (-7, -2), (-4, -1), (-1, 7), (-3, -4), (-8, 10), (-9, 6), (-9, 4), (-2, 5), (-2, 10), (8, -8), (-1, -3), (-5, 7), (9, 3), (2, -10), (7, 4), (9, 2), (-3, -2), (-2, -9), (3, 1), (-10, 7), (-6, -5), (-6, 4), (-2, 3), (2, 5), (-7, 6), (8, -6), (9, -5), (7, -2), (-5, 8), (-5, -3), (0, 0), (-1, 1), (10, 3), (2, -9), (-8, -9), (-2, -2), (6, 6), (5, 9), (1, 5), (2, 9), (-2, 0), (-10, -7), (9, 10), (2, -1), (6, -8), (1, -9), (3, -10), (9, -1), (5, 6), (7, -4), (8, -10), (0, -8), (2, 8), (-9, -7), (4, -7), (-10, 6), (10, -8), (9, 8), (-7, 8), (4, -4), (9, -3), (10, -5), (4, 7), (-8, -6), (3, -8), (8, 7), (-4, 2), (-7, 10), (-10, -2), (1, -7), (-5, -1), (1, 10), (5, 3), (-6, -4), (-5, -10), (10, 2), (7, -8), (7, 10), (-8, 6), (0, 1), (1, 2), (-3, 6), (0, 8), (7, -9), (5, 0), (-10, 0), (-10, 9), (8, 0), (-2, 4), (-6, 2), (-9, -4), (8, 3), (1, -6), (6, 5), (10, -7), (-7, -3), (0, -5), (-4, -5), (-7, -8), (3, -5), (-7, -4), (10, -2), (5, 4), (1, 0), (7, -7), (-2, 8), (-7, 7), (-2, 1), (6, -9), (-3, 7), (9, 6), (-6, -1), (-8, 5), (0, 10), (-9, 2), (-8, -4), (1, 8), (-2, -5), (-4, 8), (3, -3), (-8, 9), (-3, -3), (4, -1), (7, 6), (4, -8), (3, 10), (-10, -10), (-3, 10), (7, 0), (2, -7), (5, -7), (4, 9), (-5, -4), (-7, -7), (-7, 5), (-2, -6), (5, 5), (-5, 9), (-7, 1), (-5, -8), (2, -8), (-9, -10), (-6, -9), (1, 3), (10, 6), (8, 5), (-10, -3), (-2, -8), (4, -9), (-5, 6), (0, -4), (7, 1), (1, -8), (-9, -8), (7, 5), (6, 0), (-5, -9), (-8, -8), (-9, 7), (10, 10), (3, 5), (5, -3), (-8, -3), (-1, -4), (2, 1), (-10, -1), (-2, -10), (-1, -10), (9, 4), (-8, 7), (7, -3), (-4, 1), (-5, 3), (5, -10), (-4, 6), (8, -3), (3, 8), (-3, -9), (1, -3), (-2, 6), (7, -10), (9, 9), (-10, -5), (-5, 0), (-8, -10), (-3, 2), (0, -9), (-6, 0), (8, 1), (4, 2), (8, 2), (-4, -9), (-2, -4), (-8, 2), (-9, 0), (1, 7), (-4, 0), (0, 6), (-9, -1), (7, 9), (-1, 5), (-9, 5), (2, -6), (-4, -7), (2, -3), (4, -6), (1, -10), (-6, 8), (-3, 0), (4, 6), (4, 0), (1, 9), (10, -3), (5, 10), (0, 4), (2, 7), (6, -1), (5, 1), (4, 4), (-6, 7), (3, -4), (3, 6), (-1, -1), (-3, -10), (-9, 8), (-4, -10), (-10, -6), (-4, 10), (-6, -2), (-1, 6), (8, -1), (5, -2), (-7, 4), (7, 8), (-2, 7), (2, -4), (-10, 10), (3, -2), (8, 9), (-10, 5), (3, 0), (7, -6), (6, 3), (-9, 10), (-5, 4), (-9, 9), (2, -2), (-3, 9), (-2, 9), (-4, 3), (7, 3), (6, -10), (-6, -10), (4, 5), (1, -1), (-4, 7), (0, 9), (4, 8), (3, 7), (-10, 8), (-1, -5), (10, -9), (0, -7), (6, 8), (2, -5), (-3, -7), (5, -8)}
  5. Take(listS, 1, 1) → listA
  6. Point(listA) → A
  7. Take(listS, 4, 4) → listD
  8. Point(listD) → D
  9. Take(listS, 5, 5) → listE
  10. Point(listE) → E
  11. Take(listS, 6, 6) → listF
  12. Point(listF) → F
  13. Take(listS, 3, 3) → listC
  14. Point(listC) → C
  15. Take(listS, 2, 2) → listB
  16. Point(listB) → B
  17. Segment(A, B) → ab
  18. Segment(B, C) → bc
  19. Segment(C, A) → ca
  20. Segment(A', B') → a'b'
  21. Segment(B', C') → b'c'
  22. Segment(C', A') → c'a'
  23. Segment(C, D) → cd
  24. Segment(D, A) → da
  25. Segment(D, E) → de
  26. Segment(E, A) → ea
  27. Segment(E, F) → ef
  28. Segment(F, A) → fa
  29. Segment(C', D') → c'd'
  30. Segment(D', E') → d'e'
  31. Segment(E', F') → e'f'
  32. Segment(F', A') → f'a'
  33. Segment(E', A') → e'a'
  34. Segment(D', A') → d'a'
  35. RandomElement({"Awesome!", "Great Job!", " Correct!"}) → praise, " Correct!"
  36. If(refax ≟ "j", "x", If[refax ≟ "k", "y", If[refax ≟ "l", "x - axis and y"]]) → axis
  37. If(refax ≟ "j", (x(A), (-y(A))), If[refax ≟ "k", ((-x(A)), y(A)), If[refax ≟ "l", ((-x(A)), (-y(A)))]]) → U
  38. If(refax ≟ "j", (x(B), (-y(B))), If[refax ≟ "k", ((-x(B)), y(B)), If[refax ≟ "l", ((-x(B)), (-y(B)))]]) → V
  39. If(refax ≟ "j", (x(C), (-y(C))), If[refax ≟ "k", ((-x(C)), y(C)), If[refax ≟ "l", ((-x(C)), (-y(C)))]]) → W
  40. If(refax ≟ "j", (x(D), (-y(D))), If[refax ≟ "k", ((-x(D)), y(D)), If[refax ≟ "l", ((-x(D)), (-y(D)))]]) → X
  41. If(refax ≟ "j", (x(E), (-y(E))), If[refax ≟ "k", ((-x(E)), y(E)), If[refax ≟ "l", ((-x(E)), (-y(E)))]]) → Y
  42. If(refax ≟ "j", (x(F), (-y(F))), If[refax ≟ "k", ((-x(F)), y(F)), If[refax ≟ "l", ((-x(F)), (-y(F)))]]) → Z

AI Drawing Prompt Reference

Draw a coordinate-plane figure using integer points. Pick points A, B, C to form triangle ABC with line segments AB, BC, and CA. Add point D, E, F with additional segments CD, DA, DE, EA, EF, and FA, so the figure is a connected network of straight segments between these points. Then construct the reflected points A’, B’, C’, D’, E’, and F’ by reflecting the originals across one of the axes (x-axis, y-axis, or both). Finally, draw all the corresponding reflected segments: A’B’, B’C’, C’A’, C’D’, D’E’, E’F’, F’A’, E’A’, and D’A’. The reflected points and segments should match the original connectivity pattern under the chosen reflection.
The prompt above was compiled from the original drawing commands and is for reference only.