Xcaret Group Logo

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2020-01-25 06:47

Polygon Vector Transformation

This example demonstrates how to construct the Xcaret Group logo using GeoGebra. Key mathematical concepts include vectors, reflection, polygons, and angles. Commands such as Line, OrthogonalLine, Vector, OrthogonalVector, Midpoint, LineBisector, Mirror, Intersect, and Polygon are used to build the various parts of the logo. Suitable for high school geometry education.

GeoGebra Commands & Parameters

Line(A, B) → s
OrthogonalLine(A, s) → b
Vector(A, B) → u
OrthogonalVector(u) → v
Midpoint(A_1, A) → J
LineBisector(A, B) → m
OrthogonalLine(J, m) → i
OrthogonalLine(K, i) → l
OrthogonalLine(F, l) → n
Mirror(n, i) → n'
OrthogonalLine(A_1, b) → r
Mirror(l, m) → l'
OrthogonalLine(B, u, xOyPlane) → g
Intersect(l, n) → Q
Intersect(g, r) → C
Polygon(A_1, C, B, A) → q1, a_1, c, b_1, a_2
Intersect(l, n') → E
Line(A_1, B) → f
Mirror(G, m) → G'
Mirror(E, m) → E'
Mirror(G, f) → G'_1
Mirror(G'_1, i) → H
Mirror(E, i) → E'_1
Mirror(E'_1, m) → I
Mirror(G', i) → G''
Mirror(G, i) → G'_2
Mirror(G'', f) → G'''
Mirror(G''', i) → L
Line(A, C) → h
Line(G', h) → j
Line(L, h) → k
Line(G, f) → p
Line(G'_1, f) → q
Intersect(j, p) → D
Intersect(h, p) → M
Intersect(k, p) → N
Mirror(M, m) → M'
Mirror(N, m) → N'
Mirror(M, f) → M'_1
Mirror(N, f) → N'_1
Mirror(M', h) → M''
Intersect(m, i) → O
Polygon(O, E', L, M'') → q2, o_1, e', l_1, m''
Polygon(E', G', D, M) → q3, t, g', d, m_1
Polygon(O, M, G, E) → q4, o_2, m_2, g_1, e
Polygon(M', H, E'_1, O) → q5, m', h_1, e'_1, o_3
Polygon(O, M'_1, G'', I) → q6, o_4, m'_1, g'', i_1
Polygon(M'', N, G''', I) → q7, a, n_1, g''', i_2
Polygon(G'_1, N', M', E) → q8, g'_1, f_1, j_1, e_1
Polygon(E'_1, G'_2, N'_1, M'_1) → q9, k_1, g'_2, n'_1, p_1