Translations (1) - Geometry (Shape) for year 5 (age 9-10) by ... - Free Printable

Problem Description:

The task involves translating geometric shapes on a coordinate grid according to specific instructions. Translation means moving the shape to a new position without changing its size, orientation, or shape. The instructions specify how many units to move the shape horizontally (left/right) and vertically (up/down).

Solution Approach:

1. Understand Translation Rules:
- Moving right increases the x-coordinate.
- Moving left decreases the x-coordinate.
- Moving up increases the y-coordinate.
- Moving down decreases the y-coordinate.

2. Apply Each Translation Instruction:
For each shape, identify its initial coordinates and apply the translation rules step by step.

3. Draw the Translated Shape:
After calculating the new coordinates, plot the translated shape on the grid.

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Step-by-Step Solution:

#### Shape 1: Translate 3 units to the right
- Initial Coordinates: The shape is a small rectangle located at coordinates approximately:
- Bottom-left corner: (1, 2)
- Top-right corner: (3, 4)

- Translation: Move 3 units to the right.
- New x-coordinates: Add 3 to each x-coordinate.
- Bottom-left: (1 + 3, 2) = (4, 2)
- Top-right: (3 + 3, 4) = (6, 4)

- New Shape: Draw the rectangle with the new coordinates:
- Bottom-left: (4, 2)
- Top-right: (6, 4)

#### Shape 2: Translate 4 units down
- Initial Coordinates: The shape is a larger rectangle located at coordinates approximately:
- Bottom-left corner: (2, 5)
- Top-right corner: (6, 7)

- Translation: Move 4 units down.
- New y-coordinates: Subtract 4 from each y-coordinate.
- Bottom-left: (2, 5 - 4) = (2, 1)
- Top-right: (6, 7 - 4) = (6, 3)

- New Shape: Draw the rectangle with the new coordinates:
- Bottom-left: (2, 1)
- Top-right: (6, 3)

#### Shape 3: Translate 5 units to the left
- Initial Coordinates: The shape is a smiley face located at coordinates approximately:
- Center of the face: (4, 4)

- Translation: Move 5 units to the left.
- New x-coordinate: Subtract 5 from the x-coordinate.
- Center of the face: (4 - 5, 4) = (-1, 4)

- New Shape: Draw the smiley face with the new center at (-1, 4).

#### Shape 4: Translate 4 units up
- Initial Coordinates: The shape is a cylinder located at coordinates approximately:
- Bottom-left corner of the base: (3, 2)
- Top-right corner of the base: (5, 4)

- Translation: Move 4 units up.
- New y-coordinates: Add 4 to each y-coordinate.
- Bottom-left: (3, 2 + 4) = (3, 6)
- Top-right: (5, 4 + 4) = (5, 8)

- New Shape: Draw the cylinder with the new coordinates:
- Bottom-left of the base: (3, 6)
- Top-right of the base: (5, 8)

#### Shape 5: Translate 4 units up and 3 units to the right
- Initial Coordinates: The shape is a parallelogram located at coordinates approximately:
- Bottom-left vertex: (1, 1)
- Top-right vertex: (5, 3)

- Translation:
- Move 4 units up: Add 4 to the y-coordinates.
- Move 3 units to the right: Add 3 to the x-coordinates.
- Bottom-left: (1 + 3, 1 + 4) = (4, 5)
- Top-right: (5 + 3, 3 + 4) = (8, 7)

- New Shape: Draw the parallelogram with the new coordinates:
- Bottom-left: (4, 5)
- Top-right: (8, 7)

#### Shape 6: Translate 6 units to the left and 1 unit up
- Initial Coordinates: The shape is a trapezoid located at coordinates approximately:
- Bottom-left vertex: (2, 1)
- Top-right vertex: (6, 3)

- Translation:
- Move 6 units to the left: Subtract 6 from the x-coordinates.
- Move 1 unit up: Add 1 to the y-coordinates.
- Bottom-left: (2 - 6, 1 + 1) = (-4, 2)
- Top-right: (6 - 6, 3 + 1) = (0, 4)

- New Shape: Draw the trapezoid with the new coordinates:
- Bottom-left: (-4, 2)
- Top-right: (0, 4)

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Final Answer:

After applying all translations, the new positions of the shapes are as follows:
1. Rectangle translated 3 units to the right.
2. Rectangle translated 4 units down.
3. Smiley face translated 5 units to the left.
4. Cylinder translated 4 units up.
5. Parallelogram translated 4 units up and 3 units to the right.
6. Trapezoid translated 6 units to the left and 1 unit up.

Boxed Answer:
\[
\boxed{\text{See detailed steps above for each translated shape.}}
\]