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Plot Reflection for Any Horizontal or Vertical Line

Plot Reflection for Any Horizontal or Vertical Line
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2018-02-09 04:32
Coordinate GeometryGeometric Construction
This example demonstrates how to plot the reflection of any horizontal or vertical line. It involves core math concepts like reflection transformation, circumcircle of a circle, difference and slope, tangent function, set theory, tangent line, and geometric constructions. The construction uses commands like Polygon, Join, Point, Textfield, Segment in GeoGebra. Suitable for high school students learning coordinate geometry and transformations.

GeoGebra Commands & Parameters

  1. Polygon((10.5, 9), (25, 9), (25, -10), (10.5, -10)) → RightBox, j, k, l, m
  2. Polygon((-12, 7.4), (25, 7.4), (25, 15), (-12, 15)) → TopBox, f, g, h, i
  3. Join({Sequence[Sequence[(i, j), i, -10, 10, 1], j, -10, 10, 1], {(15, 6.5), (17, 6.5), (19, 6.5)}}) → GridSpace
  4. Point(GridSpace) → A1
  5. Point(GridSpace) → B1
  6. Point(GridSpace) → C1
  7. Polygon((14, 7.2), (14, 5.8), (20, 5.8), (20, 7.2)) → PointsBox, n, p, q, r
  8. Polygon(A, B, C) → ABC, c, a, b
  9. Polygon(A1, B1, C1) → ABC1, c1, a1, b1
  10. Polygon(Acorr, Bcorr, Ccorr) → ABCcorr, ccorr, acorr, bcorr
  11. Textfield(usertext) → InputBox1
  12. Segment(Acorr, (x(Acorr), 0)) → Ahelper1
  13. Segment(Bcorr, (x(Bcorr), 0)) → Bhelper1
  14. Segment(Ccorr, (x(Ccorr), 0)) → Chelper1
  15. Segment(Acorr, (0, y(Acorr))) → Ahelper2
  16. Segment(Bcorr, (0, y(Bcorr))) → Bhelper2
  17. Segment(Ccorr, (0, y(Ccorr))) → Chelper2
  18. Segment(R1, R2) → ReflLine
  19. Segment((0, 7.3), (0, -8)) → yaxis

AI Drawing Prompt Reference

Draw a frame consisting of three rectangles, one at the top, one at the bottom, and one in the middle. Inside the middle rectangle, place three points and connect them to form a triangle. Then, plot the horizontal and vertical reflections of this triangle and its three points, ensuring the reflected points are within the frame. Finally, draw lines connecting the midpoints of the reflected and original triangle sides, and lines from the triangle's vertices to the x-axis and y-axis.
The prompt above was compiled from the original drawing commands and is for reference only.