Plane Transformations Exploration

Name:

Date:

📐 Part 1: Transformation Basics

1. Which of the following is the most precise definition of a line segment?

A straight path that goes on forever in both directions

The part of a line between two points, including both endpoints

A curved path connecting two points

Two rays that share a common endpoint

2. A transformation that preserves both distance and angle is called:

Rigid transformation (isometry)

Non-rigid transformation

Horizontal stretch

Vertical compression

3. Which transformations preserve distance and angle? (Select all that apply)

Translation

Rotation

Reflection

Horizontal stretch

Dilation with scale factor 2

4. In transformation notation, if point A(2, 3) maps to point A'(5, 7), we can write this as:

A → A'

(2, 3) → (5, 7)

T(A) = A'

All of the above

✏️ Part 2: Analysing Transformations

5. Triangle ABC has vertices at A(1, 2), B(3, 4), and C(1, 6). After a transformation, the vertices are A'(4, 2), B'(6, 4), and C'(4, 6). Describe this transformation in words:

6. A rectangle undergoes a horizontal stretch with factor 3. If the original rectangle had dimensions 4 cm × 6 cm, what are the new dimensions?

New dimensions: _______ cm × _______ cm

Does this transformation preserve distance? _______

Does this transformation preserve angle? _______

7. Point P(−2, 5) is rotated 90° anticlockwise about the origin. What are the coordinates of P'?

P' = ( _____ , _____ )

8. Explain why a translation is considered a function. Include the terms "input" and "output" in your explanation.

🎯 Part 3: Transformation Challenge

9. Design a sequence of transformations that would map triangle DEF to triangle D'E'F'. Use the coordinate grid below to sketch your work.

Transformation sequence: ________________________________

10. Compare and contrast a rotation and a horizontal stretch. In your answer, discuss what properties are preserved or changed by each transformation.