二维向量与反射的几何作图 by Claudio Martínez Gil
几何画板及绘图内容加载中,请稍等……
①本范例演示了二维向量、反射、函数图像与几何图形的交互关系;②涉及的核心数学概念包括向量运算、函数图像绘制、反射变换、解析几何作图等;③作图要点:利用Line, Vector, OrthogonalVector, LineBisector, OrthogonalLine, Mirror, Intersect, Polygon, CircleArc等GeoGebra命令进行几何构造与变换;④适合高中数学教学,用于理解向量、反射、函数图像及优化问题的几何意义。
GeoGebra 命令及参数
Line(A, B) → sVector(A, B) → uOrthogonalVector(u) → vLineBisector(A_1, A) → lOrthogonalLine(K, s) → jLineBisector(A, B) → mLineBisector(A_1, A) → nLineBisector(A_1, A) → hOrthogonalLine(D, s) → iOrthogonalLine(A, s) → bOrthogonalLine(B, u, xOyPlane) → gMirror(i, m) → i'OrthogonalLine(A_1, b) → rIntersect(g, r) → CIntersect(b, l) → OIntersect(m, l) → LMirror(A_1, l) → D_2Mirror(A_1, l) → F_2Mirror(C, l) → C'_1OrthogonalLine(F, b) → fMirror(f, l) → f'Mirror(f, l) → f'_1Intersect(m, f) → MPolygon(A, B, C, A_1) → c1, a_1, b_1, c_1, f_1Intersect(b, f') → IOrthogonalLine(J, b) → qOrthogonalLine(R, b) → aOrthogonalLine(T, s) → eOrthogonalLine(E, s) → kIntersect(i, f) → NIntersect(j, q) → D_1Intersect(i, f') → E_1Intersect(m, f') → F_1Intersect(m, q) → G_1Mirror(N, m) → N'Mirror(F_1, m) → I_1Mirror(G_1, m) → J_1OrthogonalLine(Q, s) → tOrthogonalLine(V, s) → cIntersect(a, t) → B_1Intersect(q, e) → WIntersect(j, l) → PLine(P, M) → dIntersect(d, t) → GIntersect(c, d) → HOrthogonalLine(S, b) → pIntersect(p, k) → UOrthogonalLine(Z, b) → g_1Intersect(g_1, k) → C_1LineBisector(B_1, E_1) → h_1Intersect(h_1, p) → H_1CircleArc(H_1, B_1, E_1) → d_1LineBisector(W, B_1) → i_1Intersect(p, i_1) → K_1CircleArc(K_1, B_1, W) → k_1LineBisector(C_1, W) → j_1Intersect(j_1, j) → L_1CircleArc(L_1, C_1, W) → p_1LineBisector(G, U) → l_1LineBisector(E_1, D_1) → m_1Intersect(a, m_1) → M_1CircleArc(M_1, D_1, E_1) → q_1Intersect(l_1, l) → N_1CircleArc(N_1, U, G) → r_1LineBisector(O_1, L) → n_1Intersect(n_1, l) → P_1CircleArc(P_1, L, O_1) → s_1Polygon(D_1, S, G, U, C_1, W, B_1, E_1) → polígono1, t_1, s_2, g_2, u_1, f_2, w, h_2, i_2Polygon(O_1, H, M, L) → c2, o_1, h_3, m_2, l_2Mirror(O_1, m) → Q_1Mirror(H, m) → H'Mirror(M, m) → M'Mirror(L, m) → L'Polygon(Q_1, H', M', L') → c2', j_2, h', m', l'Mirror(d_1, m) → c_2Mirror(d_1, m) → d_2Mirror(k_1, m) → k_2Mirror(p_1, m) → p_2Mirror(q_1, m) → q_2Mirror(r_1, m) → r_2Mirror(s_1, m) → t_2Mirror(D_1, m) → R_1Mirror(S, m) → S'Mirror(G, m) → G'Mirror(U, m) → U'Mirror(C_1, m) → S_1Mirror(W, m) → W'Mirror(B_1, m) → T_1Mirror(E_1, m) → U_1Polygon(R_1, S', G', U', S_1, W', T_1, U_1) → polígono1', n_2, s', g', u', a_2, w', b_2, f_3
AI 绘图提示语参考
画一个二维向量与反射的几何构造图,包含两个向量和它们的反射线,展示向量操作、函数图像和几何形状的交互。先画出一条线段和两个向量,再求出其中一个向量的正交向量,并画出两条垂直线。接着,利用中垂线和反射变换构造多个点和几何形状,如多边形和圆弧,最终呈现一个复杂的几何图形,体现向量、反射、函数图像和解析几何的综合应用。
以上提示语为根据原始绘图命令整理而来,仅供参考。