第六步:滑动条与轨迹演示
几何画板及绘图内容加载中,请稍等……
①本范例通过滑动条演示点与线的动态关系,展示轨迹的形成过程;②涉及核心数学概念包括滑动条动画、轨迹、解析几何;③构造中运用了Line(线)、OrthogonalLine(垂线)、Point(点)、Intersect(交点)、Segment(线段)、Angle(角)、Vector(向量)、Translate(平移)等GeoGebra命令与对象;④适合高中阶段学生用于理解参数方程、动态几何及函数图像的绘制,也可用于微积分中的极限与导数可视化教学。
GeoGebra 命令及参数
Line(A, B) → aOrthogonalLine(B, a) → bOrthogonalLine(A, a) → cPoint(b) → COrthogonalLine(C, c) → dIntersect(c, d) → DSegment(D, C) → eSegment(C, B) → fSegment(B, A) → gSegment(A, D) → hAngle(A, B, C) → αAngle(C, D, A) → βAngle(D, A, B) → γAngle(B, C, D) → δSegment(D, E) → iSegment(E, F) → jSegment(F, G) → kSegment(G, H) → lSegment(H, I) → mSegment(I, J) → nSegment(J, K) → pSegment(K, L) → qSegment(L, M) → rSegment(M, C) → sVector(C, B) → uTranslate(D, u) → D'Translate(E, u) → E'Segment(D', E') → i'Translate(E, u) → E'_1Translate(F, u) → F'Segment(E'_1, F') → j'Translate(F, u) → F'_1Translate(G, u) → G'Segment(F'_1, G') → k'Translate(G, u) → G'_1Translate(H, u) → H'Segment(G'_1, H') → l'Translate(H, u) → H'_1Translate(I, u) → I'Segment(H'_1, I') → m'Translate(I, u) → I'_1Translate(J, u) → J'Segment(I'_1, J') → n'Translate(J, u) → J'_1Translate(K, u) → K'Segment(J'_1, K') → p'Translate(K, u) → K'_1Translate(L, u) → L'Segment(K'_1, L') → q'Translate(L, u) → L'_1Translate(M, u) → M'Segment(L'_1, M') → r'Translate(M, u) → M'_1Translate(C, u) → C'Segment(M'_1, C') → s'Segment(D, N) → tSegment(N, O) → a_1Segment(O, P) → b_1Segment(P, Q) → c_1Segment(Q, R) → d_1Segment(R, S) → e_1Segment(S, T) → f_1Segment(T, U) → g_1Segment(U, V) → h_1Segment(V, W) → i_1Segment(W, Z) → j_1Segment(Z, A) → k_1Vector(A, B) → vTranslate(D, v) → D'_1Translate(N, v) → N'Segment(D'_1, N') → t'Translate(N, v) → N'_1Translate(O, v) → O'Segment(N'_1, O') → l_1Translate(O, v) → O'_1Translate(P, v) → P'Segment(O'_1, P') → m_1Translate(P, v) → P'_1Translate(Q, v) → Q'Segment(P'_1, Q') → n_1Translate(Q, v) → Q'_1Translate(R, v) → R'Segment(Q'_1, R') → p_1Translate(R, v) → R'_1Translate(S, v) → S'Segment(R'_1, S') → q_1Translate(S, v) → S'_1Translate(T, v) → T'Segment(S'_1, T') → r_1Translate(T, v) → T'_1Translate(U, v) → U'Segment(T'_1, U') → s_1Translate(U, v) → U'_1Translate(V, v) → V'Segment(U'_1, V') → t_1Translate(V, v) → V'_1Translate(W, v) → W'Segment(V'_1, W') → a_2Translate(W, v) → W'_1Translate(Z, v) → Z'Segment(W'_1, Z') → b_2Translate(Z, v) → Z'_1Translate(A, v) → A'Segment(Z'_1, A') → c_2Translate(D', v) → D''
AI 绘图提示语参考
画一条线段和它的垂线,再在线段上取一点,画出这点垂足的轨迹,构成一个封闭图形。接着,以垂足为起点,沿着线段方向平移若干次,每次平移的距离相等,画出多个平移后的线段,展示动态几何中的参数变化和轨迹形成。
以上提示语为根据原始绘图命令整理而来,仅供参考。