Transformations Game
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This example uses a game format to demonstrate geometric transformations, including translation, reflection, and rotation. It involves core mathematical concepts from coordinate geometry. Using GeoGebra commands such as Point, Rotate, and Mirror, dynamic geometric figures can be constructed. Suitable for middle school and above students to learn about transformations and related concepts.
GeoGebra Commands & Parameters
Point(yAxis) → CCircle(C, D) → cPoint(c) → RotateRotate(Rotate, 120*°, C) → E'Rotate(Rotate, 90*°, C) → E'_1Mirror(Rotate, C) → E'_2Mirror(E'_1, C) → V_1Point(c) → C_2CircleArc(C, C_2, Rotate) → dAngle(C_2, C, Rotate) → αPoint(c) → U_2Rotate(U_2, 90*°, C) → V_2Rotate(U_2, -90*°, C) → W_2LaTeX(right, true, true) → text5Textfield(B1) → inputBox1Element(list1, a) → βPolygon(J, K, L) → poly1, l, j, kPolygon(J', K', L') → poly2, l_1, j_1, k_1Rotate(J, 90*°, C) → J'_3Rotate(K, 90*°, C) → K'_3Rotate(L, 90*°, C) → L'_3Polygon(J'_3, K'_3, L'_3) → poly1', l', j', k'Rotate(J, 180*°, C) → J'_1Rotate(K, 180*°, C) → K'_1Rotate(L, 180*°, C) → L'_1Polygon(J'_1, K'_1, L'_1) → poly1'_1, l'_1, j'_1, k'_1Rotate(J, -90*°, C) → J'_2Rotate(K, -90*°, C) → K'_2Rotate(L, -90*°, C) → L'_2Polygon(J'_2, K'_2, L'_2) → poly1'_2, l'_2, j'_2, k'_2Circle(C, K) → pCircle(C, L) → qCircle(C, J) → rRotate(K, γ, C) → K'_4Angle(K, C, K'_4) → δRotate(L, γ, C) → L'_4Angle(L, C, L'_4) → εRotate(J, γ, C) → J'_4Angle(J, C, J'_4) → ζPolygon(L'_4, K'_4, J'_4) → poly3, j'_4, l'_4, k'_4Mirror(K, xAxis) → K'_5Mirror(J, xAxis) → J'_5Mirror(L, xAxis) → L'_5Mirror(K, yAxis) → K'_6Mirror(J, yAxis) → J'_6Mirror(L, yAxis) → L'_6Midpoint(J, J'_5) → J_1Midpoint(K, K'_5) → K_1Midpoint(L, L'_5) → E_3Circle(K_1, K) → sCircle(J_1, J) → tCircle(E_3, L) → c_1Rotate(K, η, K_1) → K'_7Angle(K, K_1, K'_7) → θRotate(J, η, J_1) → J'_7Angle(J, J_1, J'_7) → ιRotate(L, η, E_3) → L'_7Angle(L, E_3, L'_7) → κSegment(K, K'_5) → mSegment(J, J'_5) → nSegment(L, L'_5) → a_1Line(K'_7, xAxis) → b_1Line(J'_7, xAxis) → d_1Line(L'_7, xAxis) → e_1Intersect(b_1, m) → F_3Intersect(n, d_1) → G_3Intersect(a_1, e_1) → H_3Polygon(F_3, G_3, H_3) → poly4, h_3, f_3, g_3Midpoint(K'_6, K) → I_3Circle(I_3, K) → f_1Rotate(K, η, I_3) → K'_8Angle(K, I_3, K'_8) → λSegment(K'_6, K) → g_1Line(K'_8, yAxis) → h_1Intersect(h_1, g_1) → M_3Midpoint(J, J'_6) → N_3Circle(N_3, J) → p_1Rotate(J, η, N_3) → J'_8Angle(J, N_3, J'_8) → μSegment(J'_6, J) → i_1Line(J'_8, yAxis) → m_1Intersect(i_1, m_1) → O_3Midpoint(L'_6, L) → P_3Circle(P_3, L) → q_1Rotate(L, η, P_3) → L'_8Angle(L, P_3, L'_8) → νSegment(L'_6, L) → n_1Line(L'_8, yAxis) → r_1Intersect(r_1, n_1) → Q_3Polygon(Q_3, M_3, O_3) → poly5, o_3, q_3, m_3LaTeX(wrong, true, true) → text11Point(xAxis) → L_1Mirror(pic1, xAxis) → pic1'Mirror(pic1', xAxis) → pic1''Rotate(pic1'', 90*°, C) → pic1'''Rotate(pic1', 90*°, C) → pic1''_1Textfield(Date) → inputBox2Textfield(Name) → inputBox3
AI Drawing Prompt Reference
Draw a coordinate system with a point on the y-axis, create a circle centered at this point, and take a point on the circle. Rotate this point by 120 degrees and 90 degrees around the center to get two new points. Reflect these points across the center to get two more points. Connect the original point on the circle to the rotated points with line segments, and label the angles and lengths of the segments.
The prompt above was compiled from the original drawing commands and is for reference only.