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Translation of a Point Along a Vector

Translation of a Point Along a Vector
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2015-02-12 20:33
VectorTransformationGeometric ConstructionSlider Animation
This example demonstrates the translation of a point in a plane by a vector. Key mathematical concepts include vectors and translation. It uses commands like Vector, Point, and Translate in GeoGebra. Suitable for middle school and above students learning geometric transformations.

GeoGebra Commands & Parameters

  1. Vector((12.9, 0.92), (11.5, 2)) → g
  2. Point(g) → E
  3. Polygon(A1, B1, C1_1, D1_1) → poly1, a, b, c, d
  4. Vector(A, B) → u
  5. Line(A, B) → e
  6. Intersect(e, b) → C1
  7. Intersect(e, d) → D1
  8. Segment(C1, D1) → f
  9. Translate(A1, Vector[(t * u)]) → A1'
  10. Translate(B1, Vector[(t * u)]) → B1'
  11. Translate(C1_1, Vector[(t * u)]) → C
  12. Translate(D1_1, Vector[(t * u)]) → D
  13. Polygon(A1', B1', C, D) → poly1', a1', b1', c_1, d_1
  14. Translate(P, Vector[(t * u)]) → P'
  15. Translate(C1, Vector[(t * u)]) → C1'
  16. Translate(D1, Vector[(t * u)]) → D1'
  17. Translate(A, Vector[(t * u)]) → A'
  18. Translate(B, Vector[(t * u)]) → B'
  19. Vector(A', B') → v

AI Drawing Prompt Reference

Draw a polygon with four vertices and a line passing through it, intersecting two of its sides. Connect these two intersection points to form a segment. Create a vector from one vertex of the polygon, and use a slider to control the translation distance. Translate the entire polygon, the intersection points, the segment, and the vector along the given vector by the slider amount. The result is a translated polygon with corresponding vertices, and draw a new vector from the original vector's start to the translated point to show the translation.
The prompt above was compiled from the original drawing commands and is for reference only.