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Visualizing Inequation Solutions

Visualizing Inequation Solutions
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2020-02-08 01:05
InequalityGeometric ConstructionGraphing
In collections Everything you want to know about inequalities without ever Everything you Want to Know about Inequalities (D Mentrard)
This example dynamically demonstrates how to represent the solution set of an inequality on a coordinate plane. Key math concepts include inequalities, number lines, and area representation. GeoGebra commands used in construction are Ray, Point, If, Polygon, and Sequence. Suitable for high school students learning about the geometric meaning of inequality solutions and introductory linear programming concepts.

GeoGebra Commands & Parameters

  1. Ray(A, F) → f
  2. Point(xAxis) → G
  3. Ray(A, G) → g
  4. If(b ≟ -2, 1, If[b ≟ -1, 1, 0]) → rep1
  5. Point(xAxis) → I
  6. Point(xAxis) → J
  7. Ray(A, J) → h
  8. Point(xAxis) → K
  9. Ray(A, K) → i
  10. If(b ≟ 1, 1, If[b ≟ 2, 1, 0]) → rep2
  11. Polygon(M, N, O, P) → poly1, m, n, o, p
  12. Polygon(Q, R, S, T) → poly2, q, r, s, t
  13. Polygon(U, V, W, Z) → poly3, u, v, w, z
  14. Sequence(A + (i, -1), i, 0, 200, 1) → liste1
  15. Sequence(A + (i + 1, 1), i, 0, 200, 1) → liste2
  16. Sequence(Segment[Element[liste1, i], Element[liste2, i]], i, 1, Length[liste2]) → liste3
  17. Sequence(A - (i, -1), i, 0, 200, 1) → liste4
  18. Sequence(A - (i + 1, 1), i, 0, 200, 1) → liste5
  19. Sequence(Segment[Element[liste4, i], Element[liste5, i]], i, 1, Length[liste4]) → liste6
  20. Polygon(B_1, D_1, C_1) → poly4, c_1, b_1, d_1
  21. Polygon(E_1, F_1, G_1, H_1) → poly5, e_1, f_1, g_1, h_1

AI Drawing Prompt Reference

Draw a coordinate plane and two rays f and g starting from point A, passing through points F and G respectively. Then draw two rays h and i starting from point A, passing through points J and K respectively. Based on the value of b, draw two regions representing the solution sets of inequalities using polygons. Finally, draw a series of parallel line segments to the x-axis, forming a grid, to illustrate the solution sets of the inequalities.
The prompt above was compiled from the original drawing commands and is for reference only.