共线点问题
几何画板及绘图内容加载中,请稍等……
本范例演示如何判断三个点是否共线。核心数学概念涉及解析几何中的直线方程和斜率。通过使用GeoGebra命令如Element、Point、AreCollinear等,可以构造和分析三角形的边和斜率,从而判断点是否共线。适合初中及以上学生学习几何作图和解析几何。
GeoGebra 命令及参数
Element(questionList, questionListIndex) → questionNumPoint({Element[H2:H7, questionNum], Element[I2:I7, questionNum]}) → CPoint({Element[F2:F7, questionNum], Element[G2:G7, questionNum]}) → BPoint({Element[D2:D7, questionNum], Element[E2:E7, questionNum]}) → AAreCollinear(A, B, C) → areCollinearUnicodeToLetter(10007) → xmarkUnicodeToLetter(10003) → cmarkLaTeX(("A=" * A)) → labelALaTeX(("B=" * B)) → labelBLaTeX(("C=" * C)) → labelCPolygon(A, B, (x(A), y(B))) → triangleAB, f, runAB, riseABPolygon(B, C, (x(B), y(C))) → triangleBC, g, runBC, riseBCLaTeX(runAB) → labelRunABLaTeX(runBC) → labelRunBCElement(J2:J7, questionNum) → slopeABElement(K2:K7, questionNum) → slopeBCElement(C2:C7, questionNum) → currentSlopeIf(currentSlope > 0, positiveSlopeRiseOffset, negativeSlopeRiseOffset) → riseOffsetIf(currentSlope > 0, positiveSlopeRunOffset, negativeSlopeRunOffset) → runOffsetTextfield(textUserSlopeAB) → ansBoxSlopeABTextfield(textUserSlopeBC) → ansBoxUserSlopeBCLaTeX("m_{BC}=") → labelSlopeBCLaTeX("m_{AB}=") → labelSlopeABLaTeX("\text{Do the points lie\\on the same line?}") → labelCollinearIf(areCollinear, "", " not") → collinearWordLaTeX("\text{\textbf{Question: } Do points \(A, B,\) and \(C\) lie on the same line?\\\textbf{Instructions: } Determine the slope between points \(A\) and \(B\) as well as the slope\\between points \(B\) and \(C\). Then decide if the points lie on the same line.}") → TEXTLaTeX((((("\text{Since \(m_{AB} " * collinearSymbol) * " m_{BC}\), the points do") * collinearWord) * " lie on the same line.}")) → feedbackPolygon((-15, -10), (-15, 11), (11, 11), (11, -10)) → viewBox, h, i, j, eIf(slopeAB < 0, LaTeX[(-riseAB)], LaTeX[riseAB]) → labelRiseABIf(slopeBC < 0, LaTeX[(-riseBC)], LaTeX[riseBC]) → labelRiseBC