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Find the Parallel and Perpendicular Line: Interactive Linear Equation Practice

Find the Parallel and Perpendicular Line: Interactive Linear Equation Practice
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2019-08-31 20:28
Coordinate GeometryGeometric ConstructionSlider AnimationGraphing
In collections Linear Equations Activities
This GeoGebra example demonstrates how to find the equations of lines parallel and perpendicular to a given line through interactive input boxes and randomly generated conditions. The core mathematical concepts include slope of a line, equal slopes for parallel lines, negative reciprocal slopes for perpendicular lines, and point-slope or slope-intercept forms of linear equations. Construction highlights: the Random and RandomElement commands generate random line parameters, Slope computes the slope, OrthogonalLine constructs the perpendicular line, If checks user answers, Textfield and InputBox provide interactive input, and FractionText displays slopes as fractions. Suitable for upper middle school or high school students practicing algebra and coordinate geometry, and useful for classroom demonstrations or self-paced exploration of parallel and perpendicular relationships.

GeoGebra Commands & Parameters

  1. FromBase(d_1, 10) → d_p
  2. RandomElement({1 / 2, 1 / 4, 3 / 4, -1 / 2, -1 / 4, -3 / 4}) → a
  3. Random(-6, 6) → b
  4. FromBase(n_1, 10) → n_p
  5. Textfield(n_1) → InputBox1
  6. If(a ≥ 0, n_p / d_p, ((-n_p)) / d_p) → s_p
  7. Textfield(d_1) → InputBox2
  8. Random(-6, 6) → b_2
  9. FromBase("b_2", 10) → yi_p
  10. If(b_2 ≟ b, b_2 + 1, b_2) → b_3
  11. RandomElement({-4, 4, 0}) → A_x
  12. Random(-8, 8) → b_4
  13. OrthogonalLine(G, f) → g
  14. RandomElement({-3, 3, 0}) → B_{x}
  15. Textfield(c) → InputBox3
  16. FromBase(c, 10) → c_1
  17. If(b ≥ 0, c_1, (-c_1)) → c_2
  18. If(d ≟ true ∧ b_3 ≟ c_2 ∧ a ≟ s_p, "Great Job!", "") → Sol_1
  19. If(d ≟ true ∧ s_p ≠ a ∧ d_1 ≠ "" ∧ n_1 ≠ "", "Check your slope", "") → Sol_2
  20. If(d ≟ true ∧ b_3 ≠ c_2, "Check your y-intercept", "") → Sol_3
  21. If(d ≟ true ∧ b > -1, "x +", "x -") → t_2
  22. If(e ≟ true ∧ b_4 ≥ 0, "x +", "x -") → t_3
  23. If(d ≟ true ∧ a ≥ 0, "y = ", "y = -") → t_1
  24. Slope(g) → a_1
  25. If(e ≟ true ∧ a_1 ≥ 0, "y = ", "y = -") → t_4
  26. If(b_4 ≥ 0, c_2, (-c_2)) → c_3
  27. If(e ≟ true ∧ b_4 ≠ c_3, "Check your y-intercept", "") → Sol_4
  28. If(a_1 ≥ 0, n_p / d_p, ((-n_p)) / d_p) → s_{p1}
  29. If(e ≟ true ∧ s_{p1} ≠ a_1 ∧ d_1 ≠ "" ∧ n_1 ≠ "", "Check your slope", "") → Sol_5
  30. If(e ≟ true ∧ b_4 ≟ c_3 ∧ a_1 ≟ s_{p1}, "Great Job!", "") → Sol_6
  31. FractionText(a) → a_2

AI Drawing Prompt Reference

Draw a randomly generated line and label its slope and y-intercept. Then, based on the slope of this line, draw a parallel and a perpendicular line, and calculate their equations. Display the equations of these two lines in the graph and let students verify their answers through input boxes. Finally, show all slopes in fractional form and provide corresponding feedback messages.
The prompt above was compiled from the original drawing commands and is for reference only.