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Random Coordinate Geometry Questions

Random Coordinate Geometry Questions
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2021-09-24 17:02
VectorFunctionCoordinate GeometryGeometric Construction
In collections Randomised Questions
This example demonstrates randomly generated coordinate geometry problems involving concepts like trapezoids, differential calculus, and quadratic functions. Key math concepts include coordinate geometry, vector operations, function graphing, and geometric constructions. It uses commands like RandomElement, LineBisector, Line, FractionText, OrthogonalVector, LaTeX, Circle, Tangent, Random, Element, and Text. Suitable for high school mathematics teaching and learning, ideal for practice and exploration of coordinate geometry problems.

GeoGebra Commands & Parameters

  1. RandomElement(l2) → g
  2. RandomElement(l1) → e
  3. RandomElement(l1) → f
  4. LineBisector(Segment[A, B]) → k
  5. Line(A, B) → i
  6. FractionText(Slope[i]) → text2
  7. OrthogonalVector(Segment[A, B]) → u
  8. FractionText(Slope[Line[B, C]]) → text3
  9. LaTeX("\text{Gradient of AB = }" + text2 + "\text{, gradient of BC = }" + text3 + "\text{, product is -1}") → text4
  10. Circle(A, B, C) → h
  11. Tangent(A, h) → j,
  12. Random(1, Length[l3]) → question
  13. Element(l3, question) → text1
  14. Text(Element[answers, question], D, false, true) → answer

AI Drawing Prompt Reference

On a coordinate plane, create a set of random points A, B, and C, and draw the lines corresponding to segment AB and segment BC. Add numeric labels for the slopes of AB and BC, and include a brief LaTeX-style statement indicating that the product of the gradients is −1. Construct the perpendicular bisector of segment AB and show an orthogonal vector direction related to AB for visual support. Through the three points A, B, and C, draw the circle, then draw the tangent line to the circle at point A. Finally, place a random question text and an answer text area in the layout, consistent with the generated values.
The prompt above was compiled from the original drawing commands and is for reference only.