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Straight Line - Slope and Equation

Straight Line - Slope and Equation
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2020-12-16 20:47
Coordinate GeometryGeometric ConstructionSlider Animation
This example demonstrates the slope and equation of a straight line. Key mathematical concepts include the slope and equation of a line, and how to construct them using GeoGebra commands such as If, GCD, Line, Slope, etc. Suitable for students from middle school and above to learn about linear equations and geometric constructions.

GeoGebra Commands & Parameters

  1. If(y(A) < 0, ")", "") → brY_AR
  2. If(y(A) < 0, "(", "") → brY_AL
  3. If(x(A) < 0, ")", "") → brX_AR
  4. If(x(A) < 0, "(", "") → brX_AL
  5. If(c / d < 0, "-", "") → sign
  6. GCD(c, d) → HCF
  7. If(c > 0 ∧ d > 0 ∧ HCF < 2 ∧ d ≠ 1, "", If[den ≟ 0, "= undefined", If[den ≠ 1, "=" + sign + "\frac{" + num + "}{" + den + "}", "=" + sign + num]]) → text11
  8. Line(A, B) → a
  9. Slope(a) → b
  10. OrthogonalLine(A, line) → g
  11. OrthogonalLine(B, g) → h
  12. Intersect(g, h) → C
  13. Intersect(line, g) → D
  14. Intersect(g, h) → E
  15. Intersect(h, a) → F
  16. Intersect(line, g) → G
  17. Polygon(A, C, B) → poly1, a_1, b_1, c_1
  18. Midpoint(A, C) → H
  19. Midpoint(B, C) → I

AI Drawing Prompt Reference

On a coordinate plane, place two points A and B and draw the straight line passing through them. Indicate the slope of this line and show its equation. From the line, construct a perpendicular through A, then use intersections between the line and the perpendiculars to obtain several intersection points (such as C, D, E, F, and G). Form a triangle region using A, C, and B. Mark the midpoints of segments AC and BC as H and I, using the perpendicular constructions to visually connect the slope and the line’s equation with the geometry.
The prompt above was compiled from the original drawing commands and is for reference only.