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Pythagorean Theorem with Coordinates

Pythagorean Theorem with Coordinates
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2013-08-11 06:52
Coordinate GeometryGeometric Construction
This example demonstrates how to calculate the distance between two points using coordinates, with the core mathematical concept being the Pythagorean Theorem. Using the commands from the construction summary, you can create a segment between two points, calculate the slope, draw a perpendicular line, find the intersection, and draw a polygon. Suitable for middle school students learning coordinate geometry.

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. Segment(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

Draw a right triangle ABC with A and B as the endpoints of the legs and C as the endpoint of the hypotenuse. First, draw segment AB, then draw two perpendicular lines from A and B respectively, and their intersection is point C. Next, draw a rectangle with A and C as vertices, and finally find the midpoints H and I of sides AC and BC respectively.
The prompt above was compiled from the original drawing commands and is for reference only.