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Line Gradient Self Quiz

Line Gradient Self Quiz
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2019-04-25 14:17
VectorFunctionCoordinate GeometryGeometric Construction
This example demonstrates how to dynamically illustrate the calculation and properties of line gradients using GeoGebra. The core mathematical concepts involved include the definition of slope, linear equations, vector operations, and geometric transformations. Key construction points—extracted from the «Construction Summary» below—utilize GeoGebra commands/objects such as GCD (Greatest Common Divisor), If (Conditional Judgment), OrthogonalLine (Perpendicular Line), Intersect (Intersection), Line (Line), Polygon (Polygon), Distance (Distance), Segment (Segment), Angle (Angle), Slope (Slope), Dilate (Dilation), Vector (Vector), Random (Random Number), Textfield (Text Field), RandomElement (Random Element), etc. It is suitable for middle school students and above to learn and review concepts related to slope in analytical geometry.

GeoGebra Commands & Parameters

  1. GCD(deltaY, deltaX) → GCDm
  2. GCD(numerYint, deltaX) → GCDy
  3. If(sgn(deltaY / deltaX) ≥ 0, "", "-") → textSignN
  4. If(sgn(numerYint / deltaX) > 0, "+", "-") → textSign
  5. If(deltaXR ≟ 1, textSignN + deltaYR, textSignN + "\, \frac{" + deltaYR + "}{" + deltaXR + "}") → textslopeN
  6. If(denomYintR ≟ 1, textSign + numerYintR, textSign + "\frac{" + numerYintR + "}{" + denomYintR + "}") → textYint
  7. If(denomYintR ≟ 1, If[numerYintR ≟ 1, textSign, textSign + numerYintR], textSign + "\frac{" + numerYintR + "}{" + denomYintR + "}") → textMID
  8. OrthogonalLine(B, xAxis) → a_2
  9. OrthogonalLine(A, yAxis) → c
  10. Intersect(a_2, c) → C
  11. Line(A, B) → d
  12. Polygon(A, B, C) → poly1, c_1, a_1, b_1
  13. Distance(B, C) → distanceBC
  14. Distance(A, C) → distanceAC
  15. Intersect(a_2, c) → D
  16. Segment(A, D) → e
  17. Segment(C, B) → f
  18. GCD(deltaY_1, deltaX_1) → GCDm_1
  19. If(sgn(deltaY_1 / deltaX_1) ≥ 0, "", "-") → textSignN_1
  20. If(deltaXR_1 ≟ 1, textSignN_1 + deltaYR_1, textSignN_1 + "\, \frac{" + deltaYR_1 + "}{" + deltaXR_1 + "}") → textslopeN_1
  21. Line(A_1, B_1) → d_1
  22. Angle(B, D, A) → α
  23. Segment(A, B) → g
  24. GCD(deltaY_2, deltaX_2) → GCDm_2
  25. If(sgn(deltaY_2 / deltaX_2) ≥ 0, "", "-") → textSignN_2
  26. If(deltaXR_2 ≟ 1, textSignN_2 + deltaYR_2, textSignN_2 + "\, \frac{" + deltaYR_2 + "}{" + deltaXR_2 + "}") → textslopeN_2
  27. Line(A_2, B_2) → d_2
  28. Segment(A_2, B_2) → g_1
  29. GCD(deltaY_3, deltaX_3) → GCDm_3
  30. If(sgn(deltaY_3 / deltaX_3) ≥ 0, "", "-") → textSignN_3
  31. If(deltaXR_3 ≟ 1, textSignN_3 + deltaYR_3, textSignN_3 + "\, \frac{" + deltaYR_3 + "}{" + deltaXR_3 + "}") → textslopeN_3
  32. Line(A_3, B_3) → d_3
  33. Segment(A_3, B_3) → g_2
  34. Slope(g) → h
  35. Dilate(A, If[0 < i ≤ 1, 1 - i, 0], D) → A'
  36. Vector(A, A') → u
  37. Dilate(D, If[1 < i ≤ 2, 2 - i, 0], B) → D'
  38. Vector(D, D') → v
  39. Line(A, B) → j
  40. Random(-6, 6) → randomXB
  41. Random(-8, 8) → randomXA
  42. Random(-5, 5) → randomYA
  43. Textfield(textanswer) → InputBox1
  44. If(abs(answergradient - gradientLine) < 0.005, true, If[x(A) ≟ x(B), If[textanswer ≟ "undefined" ∨ textanswer ≟ "Undefined" ∨ textanswer ≟ "UNDEFINED", true, false]]) → answercorrect
  45. RandomElement({0, 2, 3, 4, 5, 6, 7, 8}) → randomdeltay_B
  46. If(randomXA ≟ randomXB ∧ randomdeltay_B ≟ 0, 5, 0) → addXB

AI Drawing Prompt Reference

Draw a dynamic illustration showing the calculation and properties of line gradients, including two lines and their intersection points, displaying the slope formula and y-intercept, highlighting key points and vectors with different colors, and add a random line with an input box for users to calculate the slope, which will be highlighted when correct.
The prompt above was compiled from the original drawing commands and is for reference only.