Translation Of Shapes Worksheet - Free Printable

Problem Explanation:

The task involves translating geometric shapes on a coordinate grid based on given instructions. Translation means moving the shape to a new position without rotating or resizing it. Each instruction specifies how many units to move the shape horizontally (left/right) and vertically (up/down).

Solution Approach:

1. Identify the Original Shape: Locate the original shape on the grid.
2. Understand the Translation Instructions:
- Moving right increases the x-coordinate.
- Moving left decreases the x-coordinate.
- Moving up increases the y-coordinate.
- Moving down decreases the y-coordinate.
3. Apply the Translation:
- For each vertex of the shape, adjust its coordinates according to the translation instructions.
- Plot the new vertices on the grid and connect them to form the translated shape.

Detailed Solutions for Each Problem:

#### 1. 5 units down and 4 units right
- Original Shape: A rectangle in the top-left quadrant.
- Translation:
- Move each vertex 5 units down (decrease y by 5).
- Move each vertex 4 units right (increase x by 4).
- Result: The rectangle is shifted to the bottom-right part of the grid.

#### 2. 2 units left and 6 units down
- Original Shape: A rectangle in the top-right quadrant.
- Translation:
- Move each vertex 2 units left (decrease x by 2).
- Move each vertex 6 units down (decrease y by 6).
- Result: The rectangle is shifted to the bottom-left part of the grid.

#### 3. 7 units left
- Original Shape: An "M"-shaped figure in the middle-right of the grid.
- Translation:
- Move each vertex 7 units left (decrease x by 7).
- No vertical movement.
- Result: The "M" shape is shifted entirely to the left side of the grid.

#### 4. 2 units left and 3 units up
- Original Shape: A triangle in the bottom-left quadrant.
- Translation:
- Move each vertex 2 units left (decrease x by 2).
- Move each vertex 3 units up (increase y by 3).
- Result: The triangle is shifted slightly left and upwards.

#### 5. 6 units up and 8 units right
- Original Shape: A square in the bottom-left quadrant.
- Translation:
- Move each vertex 6 units up (increase y by 6).
- Move each vertex 8 units right (increase x by 8).
- Result: The square is shifted to the top-right part of the grid.

#### 6. 1 unit right and 5 units up
- Original Shape: A triangle in the bottom-center of the grid.
- Translation:
- Move each vertex 1 unit right (increase x by 1).
- Move each vertex 5 units up (increase y by 5).
- Result: The triangle is shifted slightly right and upwards.

#### 7. 3 units up and 1 unit left
- Original Shape: A pentagon-like shape in the bottom-left quadrant.
- Translation:
- Move each vertex 3 units up (increase y by 3).
- Move each vertex 1 unit left (decrease x by 1).
- Result: The shape is shifted slightly left and upwards.

#### 8. 5 units down
- Original Shape: A rectangle in the top-center of the grid.
- Translation:
- Move each vertex 5 units down (decrease y by 5).
- No horizontal movement.
- Result: The rectangle is shifted downwards, staying in the same horizontal position.

#### 9. 2 units down and 4 units left
- Original Shape: A diamond shape in the top-right quadrant.
- Translation:
- Move each vertex 2 units down (decrease y by 2).
- Move each vertex 4 units left (decrease x by 4).
- Result: The diamond is shifted downwards and to the left.

Final Answer:

The solutions are already graphed in the provided image. Each shape has been correctly translated according to the given instructions.

$$
\boxed{\text{See the provided image for the final graphs.}}
$$