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Construct a Rectangle with Given Area and Unique Coordinates

Construct a Rectangle with Given Area and Unique Coordinates
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2020-03-12 23:41
PolygonCoordinate GeometryGeometric Construction
This example demonstrates how to construct a rectangle with a specified area where all vertex coordinates are unique. Key math concepts include area calculation, coordinate geometry, and geometric construction. The construction utilizes GeoGebra commands such as Union, Polygon, Segment, SurdText, InteriorAngles, Mode, Length, RandomElement, and If. It is suitable for high school mathematics instruction, focusing on coordinate geometry and geometric construction skills.

GeoGebra Commands & Parameters

  1. Union(l3, l4) → l5
  2. Polygon(A, B, C, D) → q1, a, b, c, d
  3. Segment(D, C) → f
  4. SurdText(f) → text1
  5. Segment(A, D) → g
  6. Segment(A, B) → h
  7. Segment(B, C) → i
  8. SurdText(g) → text2
  9. SurdText(h) → text3
  10. SurdText(i) → text4
  11. InteriorAngles(q1) → α, β, γ, δ
  12. Mode(l1) → l2
  13. Length(l2) → j
  14. RandomElement(l5) → l
  15. If(j ≟ 0, "No repeated coordinates.", "Repeated coordinates exist.") → text5
  16. If(c0, "Quad is a rectangle.", "Quad is NOT a rectangle.") → text8