四种等距变换
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所属专题
geometriadinamica.es
①本范例演示了四种等距变换(反射、旋转、平移、缩放)在二维平面上的几何效果与性质;②涉及核心数学概念包括变换、对称性、向量、坐标几何、几何作图;③作图要点:运用了Ray(射线)、OrthogonalLine(垂线)、Point(点)、Distance(距离)、Min(最小值)、Circle(圆)、Intersect(交点)、Line(直线)、Vector(向量)、Length(长度)、Translate(平移)、Rotate(旋转)、CircleSector(扇形)、Angle(角度)、LineBisector(角平分线)、CircleArc(圆弧)、Mirror(镜像)等GeoGebra命令与对象;④适合高中及以上学生学习和理解几何变换及其应用。
GeoGebra 命令及参数
Ray(B, A) → iOrthogonalLine(A, i) → jPoint(j) → A1Ray(A, A1) → mDistance(A, A1) → l3Min(l3, ((a - 9.5) * l3)) → d3Circle(A, d3) → sIntersect(s, m) → W_1, K_2OrthogonalLine(K_2, m) → b_1Line(F_2, b_1) → c_1Vector(F_2, O_2) → v_1Vector(B_{18}, C_{18}) → uLength(u) → l1Min(l1, ((a - 0.5) * l1)) → d1Circle(D_1, d1) → hLine(F, u) → bCircle(F, d1) → dIntersect(d, b, 2) → E_1Vector(F, E_1) → wTranslate(pic2, w) → pic2'Min(180, ((a - 3.5) * 180)) → r1Rotate(pic3, ((-r1))°, F_1) → pic3'Ray(A, B) → eOrthogonalLine(G_1, e) → fPoint(f) → H_1Rotate(H_1, r1°, G_1) → U_1Rotate(H_1, ((-r1))°, G_1) → V_1CircleSector(G_1, V_1, H_1) → gAngle(V_1, G_1, H_1) → αOrthogonalLine(A1, j) → kMin(c, ((a - 7) * c)) → d2Circle(A, d2) → pCircle(B, d2) → qCircle(A1, d2) → rIntersect(r, k, 2) → Z_1Intersect(p, e) → A_2, I_2Intersect(q, i) → B_2, J_2Circle(A1, d3) → tRay(A1, A) → lIntersect(t, l) → C_2, L_2OrthogonalLine(W_1, m) → nLine(Z_1, m) → a_1Intersect(n, a_1) → D_2LineBisector(A, B) → d_1LineBisector(A1, A) → e_1Intersect(a_1, b_1) → E_2OrthogonalLine(F_2, c_1) → f_1Point(f_1) → H_2Length(v_1) → l4Min(l4, ((a - 10.5) * l4)) → d4Circle(H_2, d4) → k_1Line(N_2, j) → i_1Line(P_2, c_1) → j_1Circle(P_2, d4) → p_1Intersect(p_1, j_1, 1) → G_2Vector(P_2, G_2) → zTranslate(pic7, z) → pic7'Intersect(p, e, 2) → M_2Point(d_1) → Q_2CircleArc(Q_2, A, B) → g_1OrthogonalLine(M_2, e) → h_1Intersect(g_1, h_1, 1) → SIntersect(e, d_1) → S_2Mirror(S, S_2) → S'Point(e_1) → R_2CircleArc(R_2, A1, A) → q_1OrthogonalLine(L_2, j) → l_1Intersect(q_1, l_1) → TT,Intersect(j, e_1) → U_2Mirror(TT, U_2) → TT'
AI 绘图提示语参考
绘制一个包含反射、旋转、平移和缩放的几何图形。首先画出点A和B,然后通过A点画一条射线,接着画出该射线的垂线并取垂足为A1,再通过A1画一条射线。接着画出A和A1之间的距离,取最小值作为圆的半径,画出圆并找到与射线的交点W1和K2。通过W1画一条垂线,通过K2画一条平行线,找到交点F2,画出向量v1和u,取u的长度作为圆的半径,画出圆并找到与向量的交点E1,平移图形并旋转图形,画出圆弧和角度,最后画出垂线和角平分线,找到交点,完成图形。
以上提示语为根据原始绘图命令整理而来,仅供参考。