Translation Practice Game: Congruence and Scoring Checks

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2021-01-10 00:27

This GeoGebra example presents an interactive “translation practice game” that demonstrates how a geometric figure preserves congruence after being translated on the coordinate plane. It focuses on the core ideas of geometric transformations (translation), congruence (distance and shape preservation), point correspondence, and automatic correctness checking by measuring distances and applying conditional logic. Construction uses Sequence to generate coordinate lists and sets up structured point data with Flatten, Shuffle, and Take; RandomElement selects randomized targets/parameters; Point and Segment create the original figure and its translated image (e.g., A, B, C versus A', B', C'); Distance computes error metrics between expected and user-created correspondences; If applies thresholds to determine pass/fail and updates the game state such as score. It also employs interface objects like a button and text labels to show level and feedback. Suitable for middle to high school geometry or coordinate-geometry practice, especially for engaging students with interactive transformation drills.

GeoGebra Commands & Parameters

Sequence(Sequence[(i, j), i, -10, 10], j, -10, 10) → listT
Flatten(listT) → listR
Shuffle(listR) → listS, {(1, 2), (-5, 5), (1, 8), (7, 0), (-5, -3), (4, 6), (-5, 6), (7, -5), (10, 8), (0, -8), (6, -3), (-10, 8), (-1, 0), (8, -4), (2, 4), (1, 0), (-3, -3), (-7, 9), (-3, -10), (-8, -4), (0, 4), (-1, -9), (-8, -3), (0, 6), (-3, 6), (-3, 8), (2, 10), (2, -4), (1, -8), (-3, -1), (5, -1), (10, 2), (6, -9), (-8, 0), (0, 2), (-9, -1), (-2, -9), (3, 10), (-9, -3), (-10, 7), (-9, 7), (8, 0), (8, -5), (0, 3), (-9, -9), (3, -6), (-2, 10), (-5, -9), (-4, 4), (5, -9), (8, 6), (0, -2), (-9, 4), (-10, 9), (7, 2), (-7, -3), (2, 3), (-5, -7), (-2, 6), (-2, -6), (-2, 4), (-7, -2), (4, 4), (-6, -5), (8, 9), (6, 8), (3, 8), (-10, -7), (-6, -8), (-1, -10), (4, 0), (-6, 9), (-5, -6), (-10, -3), (4, 9), (9, 10), (1, -4), (-6, 8), (1, -6), (3, -9), (10, 4), (3, -5), (8, 5), (10, 9), (-2, 2), (-8, -10), (-5, -8), (-5, 3), (-1, -5), (7, -3), (3, 7), (2, 7), (-2, -1), (-10, -4), (8, -10), (5, 0), (1, -7), (-2, 7), (-4, 6), (-10, -1), (5, 1), (-1, -3), (-10, 5), (-9, 3), (3, 0), (0, -4), (-7, -4), (-7, -5), (-6, 2), (6, -6), (-1, 10), (2, 5), (-1, 3), (2, 2), (4, -6), (4, -9), (7, 5), (-4, 7), (-2, -4), (-8, 10), (8, -2), (3, -1), (-8, 6), (4, 8), (-8, -8), (2, -9), (3, 1), (-3, -4), (5, 5), (9, 4), (-9, 10), (6, 9), (0, 8), (6, 3), (10, -9), (-10, 10), (-4, 1), (-4, -3), (-9, 9), (6, -1), (-7, 0), (3, 2), (3, -8), (9, 1), (-4, 10), (10, -8), (0, 5), (10, 7), (1, 6), (-5, 8), (5, -10), (9, -7), (-6, 3), (-2, -5), (7, 7), (-2, 1), (6, 5), (-8, -7), (2, 6), (-10, -2), (-8, -2), (-8, 9), (-1, 9), (-8, 8), (-4, -10), (2, -7), (-7, 4), (1, 4), (7, -6), (2, -1), (0, -7), (-3, 2), (9, -6), (-5, -1), (10, -6), (7, 9), (-6, -6), (10, -2), (-6, 0), (-3, -8), (2, -10), (4, -8), (3, 6), (-6, 10), (8, 10), (5, 2), (-3, 0), (0, 10), (2, -3), (-3, -6), (10, -5), (7, 8), (0, -6), (4, -3), (-4, 3), (-7, 8), (1, 5), (1, 9), (-6, -7), (1, 7), (0, 0), (-1, -8), (5, 8), (1, -9), (-8, -9), (-1, -4), (-4, -5), (9, 5), (4, 10), (1, -3), (-3, 7), (3, -3), (2, 9), (-8, -1), (4, -1), (-7, 7), (10, -10), (-10, 3), (-4, 9), (-3, 4), (-7, -8), (10, -1), (-3, -5), (-6, -2), (-3, -9), (-3, 1), (-9, -6), (-9, -5), (6, 0), (-8, 3), (-6, -3), (10, 6), (-2, 0), (-6, 1), (-7, -6), (4, -2), (9, 8), (-4, -9), (6, -7), (-10, 4), (-2, -8), (-6, -10), (-4, -2), (2, -6), (-10, -10), (-1, 1), (-8, -6), (5, -8), (9, -3), (5, -2), (-4, -8), (-6, 6), (7, -1), (-3, 10), (6, 2), (4, 5), (6, 4), (8, 2), (4, 7), (-4, -4), (3, -10), (9, 0), (-9, 0), (-2, -3), (1, 10), (1, 1), (-8, 1), (-5, -4), (-4, 0), (8, 1), (10, -3), (9, -8), (1, -5), (-3, -7), (-6, 7), (-2, 9), (-7, 3), (-5, 9), (4, 2), (-3, -2), (-1, 6), (-8, 4), (-5, 10), (3, 3), (0, -9), (-9, -7), (-1, -7), (5, 9), (-8, 2), (-2, 5), (5, -5), (2, -8), (-1, 4), (-7, -1), (3, -2), (-8, -5), (6, 10), (0, -1), (5, 7), (3, 5), (7, -4), (8, -8), (5, 4), (5, 10), (7, 1), (9, 2), (7, 3), (6, -8), (8, -1), (-9, -4), (5, -7), (7, 6), (-1, 2), (3, -7), (0, 7), (0, 1), (5, -4), (6, 6), (-7, -9), (8, -6), (10, 1), (3, 9), (6, -10), (1, -2), (-4, 8), (-9, 1), (4, -7), (5, 6), (-7, 6), (-9, -2), (4, 1), (-3, 5), (6, -2), (-1, 7), (5, -3), (0, -5), (3, 4), (8, -7), (-9, 2), (-1, 8), (1, -10), (-10, -9), (-2, 8), (-6, -1), (2, -5), (8, 4), (-1, -6), (5, -6), (-6, 4), (6, -4), (-5, 4), (-5, -2), (-4, -7), (-7, 5), (-5, 0), (7, 4), (-3, 3), (-8, 5), (-9, 5), (10, -7), (4, -5), (-7, 2), (-3, 9), (9, 6), (10, 5), (2, 1), (-10, 1), (-10, -6), (8, -9), (-7, 1), (-4, -1), (-6, -9), (9, -4), (-2, -7), (-5, -5), (5, 3), (-5, 7), (-5, -10), (-5, 1), (-4, 5), (-10, 6), (-6, 5), (-2, -2), (-2, 3), (-9, 8), (1, -1), (2, 0), (9, 7), (0, -3), (-1, 5), (0, -10), (9, -10), (2, 8), (10, -4), (8, -3), (7, 10), (9, -1), (-5, 2), (1, 3), (10, 0), (-1, -2), (-10, 2), (2, -2), (0, 9), (-7, 10), (-10, -8), (7, -7), (7, -9), (9, -2), (9, -5), (-10, 0), (7, -2), (9, -9), (9, 3), (8, 8), (-4, -6), (8, 3), (6, 7), (-9, -8), (4, -4), (3, -4), (-7, -7), (-6, -4), (4, 3), (-9, 6), (8, 7), (9, 9), (-7, -10), (10, 10), (7, -8), (-1, -1), (-8, 7), (7, -10), (-9, -10), (6, -5), (6, 1), (4, -10), (-4, 2), (-2, -10), (10, 3), (-10, -5)}
Take(listS, 4, 4) → listD
Point(listD) → D
Take(listS, 4, 4) → listA'
Point(listA') → U
Take(listS, 1, 1) → listA
Point(listA) → A
Take(listS, 5, 5) → listE
Point(listE) → E
Take(listS, 6, 6) → listF
Point(listF) → F
Take(listS, 3, 3) → listC
Point(listC) → C
Take(listS, 2, 2) → listB
Point(listB) → B
Segment(A, B) → ab
Segment(B, C) → bc
Segment(C, A) → ca
Distance(X, Y) → XY
Segment(A', B') → a'b'
Segment(B', C') → b'c'
Segment(C', A') → c'a'
Segment(C, D) → cd
Segment(D, A) → da
Segment(D, E) → de
Segment(E, A) → ea
Segment(E, F) → ef
Segment(F, A) → fa
Segment(C', D') → c'd'
Segment(D', E') → d'e'
Segment(E', F') → e'f'
Segment(F', A') → f'a'
Segment(E', A') → e'a'
Segment(D', A') → d'a'
If(level ≟ 1, A' ≟ U, If[level ≟ 2, A' ≟ U ∧ B' ≟ V, If[level ≟ 3, A' ≟ U ∧ B' ≟ V ∧ C' ≟ W, If[level ≟ 4, A' ≟ U ∧ B' ≟ V ∧ C' ≟ W ∧ D' ≟ X, If[level ≟ 5, A' ≟ U ∧ B' ≟ V ∧ C' ≟ W ∧ D' ≟ X ∧ E' ≟ Y, If[level ≥ 6, A' ≟ U ∧ B' ≟ V ∧ C' ≟ W ∧ D' ≟ X ∧ E' ≟ Y ∧ F' ≟ Z]]]]]) → correct
RandomElement({"Awesome!", "Great Job!", " Correct!"}) → praise, " Correct!"

AI Drawing Prompt Reference

Draw a coordinate plane with a translation practice game. Randomly generate a set of integer coordinate points, then select six points to form a hexagon by connecting them with segments. Choose one point as the target, and translate the entire hexagon so that one of its vertices matches the target, creating a second hexagon. Additionally, select a few extra points from the original set, connect them to the original vertices to form internal auxiliary segments, and draw corresponding segments in the translated hexagon. Finally, based on whether the translated vertices match the expected targets, display encouraging feedback text, and include a button to switch difficulty levels.

The prompt above was compiled from the original drawing commands and is for reference only.