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Multiple Solutions

Multiple Solutions
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2015-05-14 16:07
VectorCoordinate GeometryGeometric Construction
This example demonstrates multiple solutions involving rational numbers and geometric constructions in the coordinate plane. Using GeoGebra commands such as Segment, Ray, and Intersect, multiple possible solutions can be constructed. Suitable for middle school and above students to learn about the existence of solutions in geometry and algebra.

GeoGebra Commands & Parameters

  1. Segment(B, C) → a
  2. Segment(B, A) → b
  3. Segment(A, D) → c
  4. Segment(D, C) → d
  5. Ray(A, P) → e
  6. OrthogonalLine(D, e) → f
  7. Intersect(f, e) → E
  8. Segment(D, E) → g
  9. Angle(A, E, D) → α
  10. Segment(A, P) → h
  11. Segment(E, P) → i
  12. CurveCartesian((t^(2) * k / (1 + t^(2))), (t * k / (1 + t^(2))), t, 0, k) → j

AI Drawing Prompt Reference

Draw a line segment BC in the coordinate plane, then draw line segments BA and AD from points B and D respectively. From point A, draw a ray AP, and then draw a line through D that is perpendicular to AP, intersecting AP at point E. Connect DE and AE, and mark the angle at E. Draw line segments AP from A and EP from E. Finally, plot a parametric curve in the coordinate system where the parameter ranges from 0 to k, with x-coordinate t squared times k divided by 1 plus t squared, and y-coordinate t times k divided by 1 plus t squared.
The prompt above was compiled from the original drawing commands and is for reference only.