Transformation Definitions and Properties

kathleenh, 13.10.2020

Inhaltsverzeichnis

  1. Rigid Motions
    1. Defining Translations
    2. Defining Rotations
    3. Defining Reflections
  2. Nonrigid Motions
    1. Dilating Line Segments - Properties
    2. Dilating Figures - Properties
  3. Summary
    1. Rigid vs Nonrigid Motions

1.

Rigid Motions

  • 1. Defining Translations
  • 2. Defining Rotations
  • 3. Defining Reflections

1.1.

Defining Translations

Move points A, B, C to change the shape of the triangle. Move point Q to change the size of vector PQ. Select or unselect 'Vectors' and 'Slope' boxes to see the vectors and slope.
Question 1
[i]Move point Q so that it is on top of point P. [/i][br][br][b]What do you notice?[/b]
Question 2
[i]Starting from (0, 0), move point Q three units left and two units up.[/i][br][br][b]What happens to A'B'C'? What is the algebraic description for this transformation.[/b]
Question 3
[b]What is true about the directed line segments AA', BB' and CC'?[/b]
Question 4
[b]Write a precise definition for a translation, using the following words or objects:[br][/b][list][*][b]Point A[/b][/*][*][b]Point A'[/b][/*][*][b]Directed line segment PQ[/b][/*][*][b]Directed line segment AA'[/b][/*][*][b]Parallel[/b][/*][*][b]Direction[/b][/*][*][b]Length[/b][/*][/list]
Question 5
[b]Which of the following are properties of the translated triangle A'B'C'?[/b]
– kathleenh

1.2.

–

1.3.

–

2.

Nonrigid Motions

  • 1. Dilating Line Segments - Properties
  • 2. Dilating Figures - Properties

2.1.

Dilating Line Segments - Properties

Question 1
[i]Leaving the center of dilation, point D, at (0, 0), point A at (0, 3) and point B at (3, 0), adjust the scale factor k to 2, 3, 4 and 5. [/i][br][br][b]What are you noticing about the slope of AB compared to A'B'?[/b]
Question 2
[i]Leaving point A at (0, 2), move point B to (4, 3) and move the center of dilation, point D, so that is is on line segment AB at (2, 3). Adjust the scale factor, k, to 0.5, 2, 3, and 4.[/i][br][b][br]What do you notice about the length and location of A'B' compared to AB?[/b]
Question 3
[b]How would you summarize the differences in the dilated line when the center of dilation is ON the preimage line versus NOT ON the preimage line?[/b]
– kathleenh

2.2.

–

3.

Summary

  • 1. Rigid vs Nonrigid Motions

3.1.

Rigid vs Nonrigid Motions

Question 1
Which transformation(s) preserve distance (segment lengths) AND angle measures?
Question 2
Which transformation(s) preserves angle measures ONLY?
Question 3
Which transformation(s) preserves orientation?
Question 4
Which transformation(s) result in congruent figures?
Question 5
Which transformation(s) result in similar, but not congruent figures?
– kathleenh

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