Plane Transformations Exploration

Name:

Date:

📐 Part 1: Understanding Transformations

Success Criteria: I can identify and describe different types of transformations

1. Which transformation preserves both distance and angle?

Translation

Horizontal stretch

Vertical compression

Non-uniform scaling

2. A point A(3, 2) is translated 4 units right and 3 units up. What are the coordinates of A'?

A'(7, 5)

A'(-1, -1)

A'(12, 6)

A'(3, 2)

3. Which transformations preserve distance but may change angles? (Select all that apply)

Rotation

Reflection

Horizontal stretch

Translation

4. On the coordinate plane below, draw triangle ABC with vertices A(1, 1), B(3, 1), and C(2, 3). Then draw its reflection across the y-axis and label it A'B'C'.

✏️ Part 2: Transformation Analysis

Success Criteria: I can describe transformations as functions and compare their properties

5. Complete the transformation rule: A translation that moves a point 5 units left and 2 units down can be written as (x, y) → (_______, _______)

6. Explain why a translation preserves both distance and angle, while a horizontal stretch does not.

7. Triangle DEF has vertices D(0, 0), E(4, 0), and F(2, 2). After a transformation, the image triangle D'E'F' has vertices D'(0, 0), E'(8, 0), and F'(4, 2). Describe this transformation and explain whether it preserves distance and angle.

8. For visual learners: Draw and label a square with side length 3 units. Show what happens to this square under each transformation:

a) Rotation 90° clockwise about the origin

b) Horizontal stretch by factor of 2

🚀 Part 3: Challenge Problem

Extension Activity: For advanced learners

9. Challenge: A point P(a, b) undergoes the following sequence of transformations:
• First: Reflection across the line y = x
• Then: Translation 3 units right and 1 unit down
• Finally: Rotation 180° about the origin

Write the final coordinates of P in terms of a and b, and determine which properties (distance, angle, or both) are preserved by this composition of transformations.

10. Real-world Connection: Describe a real-world situation where you might observe each type of transformation. Explain why understanding whether transformations preserve distance and angle matters in that context.