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Translating Shapes on Grids

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Translating Shapes on Grids

Coordinate grid with shapes

📍 Part 1: Understanding Translations

1. What happens when we translate a shape?

The shape changes size

The shape flips over

The shape slides to a new position

The shape rotates around

2. A triangle has a vertex at (3, 4). If we translate it 2 spaces right and 1 space up, what are the new coordinates?

(1, 3)

(5, 5)

(3, 6)

(5, 3)

3. Which of these describe a translation? (Check all that apply)

Moving 4 spaces left

Turning the shape upside down

Moving 3 spaces down

Making the shape bigger

📊 Part 2: Coordinate Translations

4. Complete the translation table. A rectangle has vertices at (1, 2), (4, 2), (4, 5), and (1, 5). Translate it 3 spaces right and 2 spaces down.

Original coordinates → New coordinates

(1, 2) → (_____, _____)

(4, 2) → (_____, _____)

(4, 5) → (_____, _____)

(1, 5) → (_____, _____)

5. A triangle is translated from (2, 1), (5, 1), (3, 4) to (6, 3), (9, 3), (7, 6). Describe the translation:

The triangle moved _____ spaces _____________ and _____ spaces _____________.

6. Draw and translate on the grid below:

• Plot a square with corners at (1, 1), (3, 1), (3, 3), and (1, 3)

• Translate it 4 spaces right and 1 space up

• Draw both the original and translated squares

✏️ Part 3: Problem Solving

7. A shape is at coordinates (2, 6), (5, 6), and (3, 9). After translation, it moves to (7, 4), (10, 4), and (8, 7). Write the translation rule:

Translation rule: (x, y) → (x _____ _____, y _____ _____)

8. Explain in your own words why translation is called a "slide" transformation:
9. Extension Challenge: A pentagon has vertices that all follow the rule (x, y) → (x - 3, y + 4). If one vertex ends up at (2, 7), what were its original coordinates?

Original coordinates: (_____, _____)

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