Translating Shapes Activity + Extension - Free Printable

To solve the problem, we need to describe the translation of each shape from its initial position (black) to its final position (blue). Translation involves moving a shape horizontally and/or vertically without rotating or changing its size. Let's analyze each case step by step.

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1. Square

- Initial Position (Black Square): The black square is located at coordinates approximately:
- Bottom-left corner: (3, 4)
- Top-right corner: (6, 7)

- Final Position (Blue Square): The blue square is located at coordinates approximately:
- Bottom-left corner: (8, 5)
- Top-right corner: (11, 8)

- Translation Analysis:
- Horizontal movement: The x-coordinate of the bottom-left corner changes from 3 to 8. This is a shift of \( 8 - 3 = 5 \) units to the right.
- Vertical movement: The y-coordinate of the bottom-left corner changes from 4 to 5. This is a shift of \( 5 - 4 = 1 \) unit up.

- Translation Description: The square is translated 5 units to the right and 1 unit up.

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2. Triangle

- Initial Position (Black Triangle): The black triangle is located at coordinates approximately:
- Bottom-left vertex: (4, 2)
- Top vertex: (6, 6)
- Bottom-right vertex: (8, 2)

- Final Position (Blue Triangle): The blue triangle is located at coordinates approximately:
- Bottom-left vertex: (5, 7)
- Top vertex: (7, 11)
- Bottom-right vertex: (9, 7)

- Translation Analysis:
- Horizontal movement: The x-coordinate of the bottom-left vertex changes from 4 to 5. This is a shift of \( 5 - 4 = 1 \) unit to the right.
- Vertical movement: The y-coordinate of the bottom-left vertex changes from 2 to 7. This is a shift of \( 7 - 2 = 5 \) units up.

- Translation Description: The triangle is translated 1 unit to the right and 5 units up.

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3. Trapezoid

- Initial Position (Black Trapezoid): The black trapezoid is located at coordinates approximately:
- Bottom-left vertex: (2, 2)
- Bottom-right vertex: (8, 2)
- Top-left vertex: (3, 6)
- Top-right vertex: (7, 6)

- Final Position (Blue Trapezoid): The blue trapezoid is located at coordinates approximately:
- Bottom-left vertex: (2, 4)
- Bottom-right vertex: (8, 4)
- Top-left vertex: (3, 8)
- Top-right vertex: (7, 8)

- Translation Analysis:
- Horizontal movement: The x-coordinates of all vertices remain the same. There is no horizontal shift.
- Vertical movement: The y-coordinate of the bottom-left vertex changes from 2 to 4. This is a shift of \( 4 - 2 = 2 \) units up.

- Translation Description: The trapezoid is translated 2 units up.

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4. Hexagon

- Initial Position (Black Hexagon): The black hexagon is located at coordinates approximately:
- Bottom-left vertex: (3, 2)
- Bottom-right vertex: (7, 2)
- Top-left vertex: (2, 5)
- Top-right vertex: (8, 5)
- Middle-left vertex: (3, 7)
- Middle-right vertex: (7, 7)

- Final Position (Blue Hexagon): The blue hexagon is located at coordinates approximately:
- Bottom-left vertex: (5, 3)
- Bottom-right vertex: (9, 3)
- Top-left vertex: (4, 6)
- Top-right vertex: (10, 6)
- Middle-left vertex: (5, 8)
- Middle-right vertex: (9, 8)

- Translation Analysis:
- Horizontal movement: The x-coordinate of the bottom-left vertex changes from 3 to 5. This is a shift of \( 5 - 3 = 2 \) units to the right.
- Vertical movement: The y-coordinate of the bottom-left vertex changes from 2 to 3. This is a shift of \( 3 - 2 = 1 \) unit up.

- Translation Description: The hexagon is translated 2 units to the right and 1 unit up.

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Final Answers

1. Square: Translated 5 units to the right and 1 unit up.
2. Triangle: Translated 1 unit to the right and 5 units up.
3. Trapezoid: Translated 2 units up.
4. Hexagon: Translated 2 units to the right and 1 unit up.

\[
\boxed{
\begin{array}{l}
1. \text{5 units to the right and 1 unit up} \\
2. \text{1 unit to the right and 5 units up} \\
3. \text{2 units up} \\
4. \text{2 units to the right and 1 unit up}
\end{array}
}
\]