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Making Scaled Copies: IM 7.1.3 Practice

Making Scaled Copies: IM 7.1.3 Practice
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2020-07-20 15:27
PolygonVectorTransformationGeometric ConstructionSlider Animation
① This example demonstrates how to create a scaled copy of a geometric figure using construction tools, visually illustrating the process of similar figures through translation and scaling. ② Core mathematical concepts include proportional scaling, similarity, translation transformations, and the application of vector directions to understand how scale factors affect the size of shapes. ③ Construction highlights: from the summary, the GeoGebra commands used include Point, UnitOrthogonalVector, UnitVector, and Polygon, with multiple points (A_1 to A_6, A, B) and polygon poly1 created, along with several image objects (pic1 to pic15) as auxiliary materials; vectors v and u control the scaling and translation directions. ④ Suitable for middle school (Grade 7) practice sessions, reinforcing concepts of scale and similar figures, and can serve as an interactive demonstration for teachers or student exploration.

GeoGebra Commands & Parameters

  1. Point(Circle[A_1, ruler]) → A_6
  2. UnitOrthogonalVector(Segment[A_1, A_6]) → v
  3. UnitVector(Segment[A_1, A_6]) → u
  4. Polygon(A_1, A_2, A_3, A_4, A_5, A_6) → poly1, a_3, a_4, a_5, a_6, a_7, a_8

AI Drawing Prompt Reference

Draw a hexagon and show how to create a scaled copy of it using translation and scaling. Start by drawing a hexagon, then create a line segment from one vertex to the opposite vertex. Based on this segment, generate a unit orthogonal vector and a unit vector to represent the scaling and translation directions. Use these vectors to translate and scale the hexagon, creating a new one that visually demonstrates the formation of similar figures.
The prompt above was compiled from the original drawing commands and is for reference only.