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Fix-a-Photo (Similar Rectangles)

Fix-a-Photo (Similar Rectangles)
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2017-02-26 08:11
FunctionCoordinate GeometryGeometric ConstructionSlider Animation
Explore the relationship between width and height of a picture on a coordinate graph, seeing how the ratio of width to height is related to the slope. This example demonstrates similar rectangles in a coordinate plane, involving core concepts like coordinate geometry, similar triangles, linear functions, and slope. Constructed using commands like Polygon, RotateText, Sequence, Text, Textfield, Segment in GeoGebra. Suitable for middle school and above to understand geometric transformations and function graphs.

GeoGebra Commands & Parameters

  1. Polygon(A, (x(drag), 0), (x(drag), y(drag)), (0, y(drag))) → preImageOutline, seg_1, photo1seg2, photo1seg1, seg
  2. RotateText("height (in.)", π / 2) → labelY
  3. Sequence(Segment[(0, k), (1000, k)], k, 0, 1000, 1) → gridHoriz
  4. Sequence(Segment[(k, 0), (k, 1000)], k, 0, 1000, 1) → gridVert
  5. Text("width (in.)", (12, -1.25)) → labelX
  6. Textfield(height) → heightInput
  7. Textfield(width) → widthInput
  8. Segment(C, (x(B), y(C))) → photo2seg3
  9. Segment(B, (x(B), y(C))) → photo2seg4
  10. Segment((x(C), y(B)), C) → photo2seg2
  11. Segment(B, (x(C), y(B))) → photo2seg1'
  12. Segment(B + (0, -0.03), (x(C), y(B) - 0.03)) → photo2seg1
  13. Segment((x(C) + 0.03, y(B)), C + (0.03, 0)) → photo2seg2'
  14. Segment(C + (0, 0.03), (x(B), y(C) + 0.03)) → photo2seg3'
  15. Segment(B + (-0.03, 0), (x(B) - 0.03, y(C))) → photo2seg4'

AI Drawing Prompt Reference

Draw a coordinate plane with a draggable rectangle representing a photo, anchored at the origin with its opposite corner movable. Fill the rectangle with a semi-transparent color and show input fields for its width and height. To the right and above, draw a larger similar rectangle with dashed edges to illustrate the constant width-to-height ratio. Cover the plane with fine grid lines, label the horizontal axis 'width (in.)' and the vertical axis 'height (in.)' with the latter rotated 90 degrees. Mark corresponding sides of both rectangles with short segments to highlight their similarity. The graph should help explore how the ratio relates to slope.
The prompt above was compiled from the original drawing commands and is for reference only.