Answer key for a math worksheet on translating shapes on a coordinate plane, displaying nine examples with translations such as "5 units down and 4 units right" and "2 units left and 6 units down."

This worksheet is about translating shapes on a coordinate grid. A *translation* means moving a shape without rotating or resizing it—just shifting it in a certain direction by a specific number of units.

The goal is to graph the image (the new position) of each shape after applying the given translation.

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🔍 How to Translate Shapes:

To translate a shape:
1. Identify the coordinates of each vertex (corner) of the original shape.
2. Apply the translation rule to each vertex:
- Right → Add to x-coordinate
- Left → Subtract from x-coordinate
- Up → Add to y-coordinate
- Down → Subtract from y-coordinate
3. Plot the new points and connect them to form the translated image.

Let’s go through each problem briefly:

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✔ Problem 1: 5 units down and 4 units right

- Move every point:
$$(x, y) \to (x + 4, y - 5)$$
- The red shape is the translated image.

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✔ Problem 2: 2 units left and 6 units down

- Rule: $$(x, y) \to (x - 2, y - 6)$$
- The red shape shows the result.

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✔ Problem 3: 7 units left

- Rule: $$(x, y) \to (x - 7, y)$$
- The red shape is shifted far to the left.

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✔ Problem 4: 2 units left and 3 units up

- Rule: $$(x, y) \to (x - 2, y + 3)$$
- The red triangle is moved left and up.

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✔ Problem 5: 6 units up and 8 units right

- Rule: $$(x, y) \to (x + 8, y + 6)$$
- The red square is moved far right and up.

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✔ Problem 6: 1 unit right and 5 units up

- Rule: $$(x, y) \to (x + 1, y + 5)$$
- The red triangle is shifted slightly right and upward.

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✔ Problem 7: 3 units up and 1 unit left

- Rule: $$(x, y) \to (x - 1, y + 3)$$
- The red arrow-like shape is moved up and slightly left.

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✔ Problem 8: 5 units down

- Rule: $$(x, y) \to (x, y - 5)$$
- The red shape is directly below the original.

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✔ Problem 9: 2 units down and 4 units left

- Rule: $$(x, y) \to (x - 4, y - 2)$$
- The red diamond-shaped figure is moved down and left.

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🧠 Key Concepts:

- Translation preserves size, shape, and orientation.
- Only the position changes.
- Use the coordinate system carefully:
- Right = +x
- Left = -x
- Up = +y
- Down = -y

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✔ Final Answer:

All the red shapes shown in the worksheet are correct translations of the original black shapes based on the given rules. This is an answer key, so the red shapes are the correct answers.

If you were solving this yourself, you would:
1. Pick each vertex of the original shape.
2. Apply the translation vector.
3. Plot the new points and draw the image.

✔ All solutions are correctly illustrated in red.

Let me know if you'd like a step-by-step walkthrough for any specific problem!