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Vectors and Components Practice

Vectors and Components Practice
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2014-06-28 23:34
VectorCoordinate GeometryGeometric Construction
This example demonstrates how to find vector components through an interactive test. Core math concepts include vector decomposition, coordinate geometry, and the Pythagorean theorem. It is constructed using commands like Shuffle, Element, Textfield, Corner, onboardingTextOffset, Polygon, Segment, Vector, Translate, and involves objects such as countQuestion, allCaseNum, allCompX, allCompY, etc. Suitable for high school students learning vectors and analytical geometry.

GeoGebra Commands & Parameters

  1. Shuffle({1, 2, 3, 4, 5, 6, 7}) → allCaseNum, {6, 7, 5, 1, 2, 3, 4}
  2. Shuffle(Sequence[t, t, -6, 6, 1] \ {-1, 1}) → allCompX, {-3, -4, -2, -5, 3, 6, 2, -6, 5, 4, 0}
  3. Shuffle(Sequence[t, t, -6, 6, 1] \ {0, -1, 1}) → allCompY, {-2, -4, -5, 2, -6, 5, 6, 4, -3, 3}
  4. Shuffle(Join[Sequence[Sequence[(j, k), j, -4, 4, 1], k, -4, 4, 1]]) → startGrid, {(1, -2), (-4, 3), (-2, -3), (-3, 1), (-4, -3), (-2, -1), (-2, 2), (4, 0), (-3, 3), (2, 1), (-1, -3), (1, 1), (4, -4), (2, -3), (2, 0), (0, 3), (-2, -4), (0, 2), (-1, -4), (-3, -3), (-2, -2), (3, 2), (1, 0), (4, -3), (0, 0), (0, -2), (-4, 4), (2, -4), (-1, -1), (3, 0), (-1, 0), (0, -3), (2, -2), (4, -1), (-1, 1), (-1, 3), (3, 1), (-4, 1), (3, -3), (4, 1), (1, -1), (1, 3), (1, -4), (-4, 2), (4, 2), (-1, 2), (1, 4), (-1, -2), (-3, -1), (-2, 0), (2, 2), (4, -2), (-2, 3), (2, 3), (-4, -2), (-4, -4), (2, -1), (3, -2), (3, -4), (-3, 0), (4, 3), (-3, -4), (1, 2), (0, 1), (4, 4), (-3, -2), (0, -1), (-1, 4), (0, -4), (-2, 4), (3, 3), (2, 4), (-3, 4), (-4, 0), (-4, -1), (-2, 1), (3, 4), (-3, 2), (3, -1), (1, -3), (0, 4)}
  5. Element(allCaseNum, Mod[countQuestion, Length[allCaseNum]] + 1) → caseNum
  6. Element(allCompX, Mod[countQuestion, Length[allCompX]] + 1) → compX
  7. Element(allCompY, Mod[countQuestion, Length[allCompY]] + 1) → compY
  8. Element(startGrid, Mod[countQuestion, Length[startGrid]] + 1) → V1
  9. Textfield(inputB) → InputBoxB
  10. Corner(5) → layoutAppSize
  11. onboardingTextOffset(Corner[onboardingText, 1], Corner[onboardingText, 3], onboardingCase, Corner[1], Corner[3], Corner[5]) → OnboardingTextOffset
  12. Textfield(inputA) → InputBoxA
  13. Textfield(inputC) → InputBoxC
  14. Polygon(P1, Mirror[P1, yAxis], Mirror[P1, (0, 0)], Mirror[P1, xAxis]) → peep, p1, f, g, h
  15. Segment((-10.8, 0), (10.8, 0)) → fakeX
  16. Segment((0, -10.8), (0, 10.8)) → fakeY
  17. Vector(V1, V2) → givenVec
  18. Vector(V1, (0, 0)) → aniVec
  19. Translate(V1, Vector[(aniSli * aniVec)]) → V1T
  20. Translate(V2, Vector[(aniSli * aniVec)]) → V2T
  21. Vector(V1T, V2T) → transVec
  22. Segment(V2T, (0, y(V2T))) → projY
  23. Segment(V2T, (x(V2T), 0)) → projX
  24. Segment((compX, 0), (0, 0)) → segmX
  25. Segment((0, compY), (0, 0)) → segmY

AI Drawing Prompt Reference

Draw a vector in a coordinate system with a random endpoint, and display its x and y components. Start by drawing the coordinate axes, then randomly select a point as the vector's endpoint and draw the vector. Next, draw perpendicular lines from the vector's endpoint to the x-axis and y-axis, marking the intersections as the endpoints of the x and y components. Finally, draw the x and y components and label their lengths.
The prompt above was compiled from the original drawing commands and is for reference only.