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Linear Inequalities System Region Selection Practice

Linear Inequalities System Region Selection Practice
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2020-01-16 08:10
Coordinate GeometryInequalityGraphing
This example demonstrates how to use GeoGebra to plot the solution region of a system of linear inequalities; core math concepts include linear inequalities and region representation; construction highlights involve commands like RandomElement, Random, GCD, If, Simplify, and objects such as qlist, q1, plist, p1, b, q2, p2, a, c2, d2, xmin, c1, d1, xmax, ymin, ymax, eq1, eq2, f, c, d, e, r1text, r2text, r3text, r4text, question, rtext, text1, corr, start, button1, A, B, goal, text3, text5, button2, incorr, button3; suitable for high school students practicing and understanding the geometric meaning of linear inequalities systems.

GeoGebra Commands & Parameters

  1. RandomElement(qlist) → q1
  2. RandomElement(plist) → p1
  3. Random(-4, 12) → b
  4. Random(-4, 7) → a
  5. GCD({p2, q2, c2}) → d2
  6. GCD({p1, q1, c1}) → d1
  7. If(q2 < 0, Simplify[(((-q2)) / d2 * y) + (p2 / d2 * x) < ((-c2)) / d2], Simplify[(q2 / d2 * y) - (p2 / d2 * x) < c2 / d2]) → f
  8. Simplify((q1 / d1 * y) - (p1 / d1 * x) < c1 / d1) → c
  9. Simplify((q1 / d1 * y) - (p1 / d1 * x) > c1 / d1) → d
  10. If(q2 < 0, Simplify[(((-q2)) / d2 * y) + (p2 / d2 * x) > ((-c2)) / d2], Simplify[(q2 / d2 * y) - (p2 / d2 * x) > c2 / d2]) → e
  11. If(eq1 ≟ eq2, RandomElement[{1, 4}], Random[1, 4]) → question
  12. If(question ≟ 1, r1text, If[question ≟ 2, r2text, If[question ≟ 3, r3text, r4text]]) → rtext

AI Drawing Prompt Reference

Draw a coordinate plane showing the solution region of a system of two linear inequalities. Two boundary lines are defined by random coefficients and constants, simplified to lowest terms. The graph includes four possible regions (combinations of inequality directions), each shaded or colored differently. One region is randomly selected as the correct answer, indicated by a text prompt. The interface includes start, reset, and feedback buttons for practice. Clearly display the boundary lines, intersection, axis ticks, and question text.
The prompt above was compiled from the original drawing commands and is for reference only.