动态斜率示例
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这个范例展示了如何动态地调整直线的斜率。核心数学概念包括直线的斜率和解析几何。通过使用GeoGebra命令如GCD、If、Slope等,可以直观地理解斜率的概念。适合初中及以上学生学习直线方程和几何作图。
GeoGebra 命令及参数
GCD(deltaY, deltaX) → GCDmGCD(numerYint, deltaX) → GCDyIf(sgn(deltaY / deltaX) ≥ 0, "", "-") → textSignNIf(sgn(numerYint / deltaX) > 0, "+", "-") → textSignIf(deltaXR ≟ 1, textSignN + deltaYR, textSignN + "\, \frac{" + deltaYR + "}{" + deltaXR + "}") → textslopeNIf(denomYintR ≟ 1, textSign + numerYintR, textSign + "\frac{" + numerYintR + "}{" + denomYintR + "}") → textYintIf(denomYintR ≟ 1, If[numerYintR ≟ 1, textSign, textSign + numerYintR], textSign + "\frac{" + numerYintR + "}{" + denomYintR + "}") → textMIDOrthogonalLine(B, xAxis) → a_2OrthogonalLine(A, yAxis) → cIntersect(a_2, c) → CLine(A, B) → dPolygon(A, B, C) → poly1, c_1, a_1, b_1Distance(B, C) → distanceBCDistance(A, C) → distanceACIntersect(a_2, c) → DSegment(A, D) → eSegment(C, B) → fGCD(deltaY_1, deltaX_1) → GCDm_1If(sgn(deltaY_1 / deltaX_1) ≥ 0, "", "-") → textSignN_1If(deltaXR_1 ≟ 1, textSignN_1 + deltaYR_1, textSignN_1 + "\, \frac{" + deltaYR_1 + "}{" + deltaXR_1 + "}") → textslopeN_1Line(A_1, B_1) → d_1Angle(B, D, A) → αSegment(A, B) → gGCD(deltaY_2, deltaX_2) → GCDm_2If(sgn(deltaY_2 / deltaX_2) ≥ 0, "", "-") → textSignN_2If(deltaXR_2 ≟ 1, textSignN_2 + deltaYR_2, textSignN_2 + "\, \frac{" + deltaYR_2 + "}{" + deltaXR_2 + "}") → textslopeN_2Line(A_2, B_2) → d_2Segment(A_2, B_2) → g_1GCD(deltaY_3, deltaX_3) → GCDm_3If(sgn(deltaY_3 / deltaX_3) ≥ 0, "", "-") → textSignN_3If(deltaXR_3 ≟ 1, textSignN_3 + deltaYR_3, textSignN_3 + "\, \frac{" + deltaYR_3 + "}{" + deltaXR_3 + "}") → textslopeN_3Line(A_3, B_3) → d_3Segment(A_3, B_3) → g_2Slope(g) → hDilate(A, If[1 < i ≤ 2, 2 - i, 0], D) → A'Vector(A, A') → uDilate(D, If[0 < i ≤ 1, 1 - i, 0], B) → D'Vector(D, D') → vLine(A, B) → jIf(GCD[deltaX, deltaY] > 1, false, true) → lowest