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Area of a Parallelogram - Coordinate Geometry

Area of a Parallelogram - Coordinate Geometry
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2015-02-03 04:15
PolygonVectorCoordinate GeometryGeometric Construction
This example demonstrates how to derive the area formula for a parallelogram by comparing the areas of two parallelograms with a vertex at (0,0). Core math concepts include coordinate geometry, vectors, and the relationship between triangle area and parallelogram area. Construction highlights the use of GeoGebra commands like Intersect, Line, Polygon, PointIn, OrthogonalLine, Segment, Distance, enhancing understanding through dynamic visualization. Suitable for high school coordinate geometry instruction and learning.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Line(A, B) → a
  3. Line(C, a) → b
  4. Line(A, C) → c
  5. Line(B, c) → d
  6. Intersect(b, d) → D
  7. Polygon(A, B, D, C) → ABCD, a_1, b_1, d_1, c_1
  8. Intersect(b, yAxis) → E
  9. Line(B, yAxis) → e
  10. Intersect(b, e) → F
  11. Polygon(A, E, F, B) → ABFE, a_2, e_1, f, b_2
  12. PointIn(ABCD) → Pointpoly1
  13. PointIn(ABFE) → Pointpoly2
  14. OrthogonalLine(F, yAxis) → k
  15. Intersect(k, yAxis) → G
  16. Segment(G, F) → height
  17. Segment(E, A) → base
  18. Distance(F, height) → distanceFheight
  19. Distance(F, G) → distanceFG

AI Drawing Prompt Reference

Draw a parallelogram ABCD and another parallelogram ABFE sharing the same base AB. First, draw a line a through points A and B, then draw line b through point C and line a, followed by drawing line c through points A and C, and finally draw line d through points B and c, with their intersection point D being the vertex of parallelogram ABCD. Next, draw line e through point B and the y-axis, with their intersection point F being the vertex of parallelogram ABFE. Then, draw a line k perpendicular to the y-axis through point F, with their intersection point G being the height of parallelogram ABFE. Finally, connect points F and G to get the height and base AB of parallelograms ABCD and ABFE.
The prompt above was compiled from the original drawing commands and is for reference only.