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Collinear Points Problem

Collinear Points Problem
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2019-02-08 23:47
VectorCoordinate GeometryGeometric Construction
This example demonstrates how to determine if three points are collinear. Key mathematical concepts include the equation of a line and slope in coordinate geometry. Using GeoGebra commands such as Element, Point, and AreCollinear, the example constructs and analyzes the sides and slopes of a triangle to determine collinearity. Suitable for students in middle school and above learning geometric construction and coordinate geometry.

GeoGebra Commands & Parameters

  1. Element(questionList, questionListIndex) → questionNum
  2. Point({Element[H2:H7, questionNum], Element[I2:I7, questionNum]}) → C
  3. Point({Element[F2:F7, questionNum], Element[G2:G7, questionNum]}) → B
  4. Point({Element[D2:D7, questionNum], Element[E2:E7, questionNum]}) → A
  5. AreCollinear(A, B, C) → areCollinear
  6. UnicodeToLetter(10007) → xmark
  7. UnicodeToLetter(10003) → cmark
  8. LaTeX(("A=" * A)) → labelA
  9. LaTeX(("B=" * B)) → labelB
  10. LaTeX(("C=" * C)) → labelC
  11. Polygon(A, B, (x(A), y(B))) → triangleAB, f, runAB, riseAB
  12. Polygon(B, C, (x(B), y(C))) → triangleBC, g, runBC, riseBC
  13. LaTeX(runAB) → labelRunAB
  14. LaTeX(runBC) → labelRunBC
  15. Element(J2:J7, questionNum) → slopeAB
  16. Element(K2:K7, questionNum) → slopeBC
  17. Element(C2:C7, questionNum) → currentSlope
  18. If(currentSlope > 0, positiveSlopeRiseOffset, negativeSlopeRiseOffset) → riseOffset
  19. If(currentSlope > 0, positiveSlopeRunOffset, negativeSlopeRunOffset) → runOffset
  20. Textfield(textUserSlopeAB) → ansBoxSlopeAB
  21. Textfield(textUserSlopeBC) → ansBoxUserSlopeBC
  22. LaTeX("m_{BC}=") → labelSlopeBC
  23. LaTeX("m_{AB}=") → labelSlopeAB
  24. LaTeX("\text{Do the points lie\\on the same line?}") → labelCollinear
  25. If(areCollinear, "", " not") → collinearWord
  26. LaTeX("\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.}") → TEXT
  27. LaTeX((((("\text{Since \(m_{AB} " * collinearSymbol) * " m_{BC}\), the points do") * collinearWord) * " lie on the same line.}")) → feedback
  28. Polygon((-15, -10), (-15, 11), (11, 11), (11, -10)) → viewBox, h, i, j, e
  29. If(slopeAB < 0, LaTeX[(-riseAB)], LaTeX[riseAB]) → labelRiseAB
  30. If(slopeBC < 0, LaTeX[(-riseBC)], LaTeX[riseBC]) → labelRiseBC