Translations - from Words | PDF printable Geometry Worksheets - Free Printable

Let's solve each problem in Section A of the worksheet titled *"Translations - In Words"*. The goal is to describe how Shape A (the original object) has been translated (moved) to reach the new position, using words like "left", "right", "up", or "down" and specifying the number of units.

We'll go through each question one by one. Since the grid is made of squares, we count the number of squares moved horizontally (left/right) and vertically (up/down).

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1)

- Shape A (gray rectangle) moves to the orange rectangle.
- Counting from the left edge: it moves 4 squares to the right.
- No vertical movement.
- ✔ Translation: 4 squares to the right.

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2)

- Gray shape A is above the orange shape.
- It moves down.
- Counting: from top of gray to top of orange = 5 squares down.
- ✔ Translation: 5 squares down.

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3)

- Gray shape A is above and slightly to the left of the orange shape.
- Move from A to the orange:
- Horizontally: 1 square to the right
- Vertically: 4 squares down
- ✔ Translation: 1 square to the right and 4 squares down.

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4)

- Gray rectangle A moves to blue rectangle.
- Move from A to blue:
- Horizontally: 6 squares to the right
- Vertically: no change
- ✔ Translation: 6 squares to the right.

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5)

- Gray diamond A is on the right; blue diamond is on the left.
- From A to blue:
- Move left by 3 squares
- Move up by 2 squares
- ✔ Translation: 3 squares to the left and 2 squares up.

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6)

- Gray L-shaped figure A moves to blue L-shape.
- From A to blue:
- Move right by 3 squares
- Move down by 3 squares
- ✔ Translation: 3 squares to the right and 3 squares down.

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7)

- Green triangle is above, gray triangle (A) is below.
- From green to A (but A is the original), so we need to go from A to green?
Wait — let’s clarify:

- The gray triangle is labeled A, and the green triangle is the image.
- So we are moving from A (gray) to green triangle.
- From A to green:
- Move left by 3 squares
- Move up by 6 squares
- ✔ Translation: 3 squares to the left and 6 squares up.

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8)

- Gray star is labeled A; green star is the image.
- From A to green:
- Move right by 2 squares
- Move down by 1 square
- ✔ Translation: 2 squares to the right and 1 square down.

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9)

- Gray curved shape (quarter circle) is labeled A.
- Green shape is the image.
- From A to green:
- Move right by 5 squares
- Move down by 5 squares
- ✔ Translation: 5 squares to the right and 5 squares down.

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✔ Final Answers:

1) 4 squares to the right
2) 5 squares down
3) 1 square to the right and 4 squares down
4) 6 squares to the right
5) 3 squares to the left and 2 squares up
6) 3 squares to the right and 3 squares down
7) 3 squares to the left and 6 squares up
8) 2 squares to the right and 1 square down
9) 5 squares to the right and 5 squares down

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🔍 Explanation:

In geometry, a translation means sliding a shape without rotating or resizing it. We describe it by how many units it moves horizontally (left/right) and vertically (up/down). We always compare the original shape (A) to the new image.

To find the translation:
1. Pick a point on Shape A (e.g., bottom-left corner).
2. Find the corresponding point on the new shape.
3. Count how many squares it moved right/left and up/down.

This method works for any shape — even irregular ones — as long as they are congruent and only moved (not rotated or reflected).

Let me know if you'd like this turned into a printable answer key!