2D Shape Transformations

Name:

Date:

📍 Part 1: Identifying Transformations

1. A triangle moves from coordinates A(2,3), B(4,3), C(3,5) to A'(5,1), B'(7,1), C'(6,3). What transformation occurred?

Translation by (3, -2)

Reflection across the x-axis

Rotation 90° clockwise

Scaling by factor 2

2. Which properties remain unchanged (invariant) after a rotation? Select all that apply.

Side lengths

Angle measures

Position on grid

Shape of the figure

3. A square is reflected across the y-axis, then scaled by factor 1/2. The final image will be:

Smaller and in the same position

Same size but flipped

Smaller and flipped to opposite side of y-axis

Larger and rotated

4. Point P(4, -2) is rotated 180° about the origin. The new coordinates are:

(-4, 2)

(4, 2)

(-4, -2)

(2, -4)

🔄 Part 2: Applying Transformations

5. Complete the transformation sequence. Starting point: A(3, 2)

Step 1: Translate by (-1, 4) → A' = ( _____ , _____ )

Step 2: Reflect A' across the x-axis → A'' = ( _____ , _____ )

6. A rectangle has vertices at (1,1), (3,1), (3,4), and (1,4). After scaling by factor 3, the new vertices will be:

7. Describe in words what transformation maps triangle ABC to triangle A'B'C' if:

A(2,3) → A'(2,-3), B(5,1) → B'(5,-1), C(4,6) → C'(4,-6)

8. Draw the result of the given transformation on the coordinate grid below:

Transform the L-shaped figure by: Rotation 90° anticlockwise about the origin, then translation by (2, -1)

🧠 Part 3: Reasoning and Problem Solving

9. A composite shape (rectangle joined to a triangle) undergoes the following transformations: reflection across y = x, then scaling by factor 2. Explain what happens to the area and perimeter of the shape.

10. Create your own transformation sequence that would move a shape from the first quadrant to the third quadrant. Use coordinate notation to describe each step.

11. True or False: When you combine a translation with a rotation, the order of transformations doesn't matter - you get the same final result. Explain your reasoning with an example.