Translations math worksheet for Grade 6, featuring four exercises with shapes moved on coordinate planes.

Let's solve each of the translation problems shown in the worksheet. A translation is a type of transformation that moves every point of a shape the same distance in the same direction.

We'll go through each quadrant and determine how to move the given shape according to the instructions.

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🔹 Top Left: Translate 4 units right

- Shape: A triangle located at the bottom-left.
- Original coordinates (approximate):
- The triangle has vertices at:
- (-4, -4)
- (-3, -4)
- (-3.5, -3)

- Translation: Move 4 units to the right → Add 4 to the x-coordinate of each point.

New coordinates:
- (-4 + 4, -4) = (0, -4)
- (-3 + 4, -4) = (1, -4)
- (-3.5 + 4, -3) = (0.5, -3)

- ✔ Draw the new triangle with these points: (0, -4), (1, -4), (0.5, -3)

> This will place the triangle near the origin, on the right side of the y-axis.

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🔹 Top Right: Translate 3 right and 2 down

- Shape: A square at (-4, 4)
- Original coordinates:
- The square has corners at:
- (-4, 4)
- (-3, 4)
- (-3, 3)
- (-4, 3)

- Translation: 3 right → add 3 to x; 2 down → subtract 2 from y

New coordinates:
- (-4 + 3, 4 - 2) = (-1, 2)
- (-3 + 3, 4 - 2) = (0, 2)
- (-3 + 3, 3 - 2) = (0, 1)
- (-4 + 3, 3 - 2) = (-1, 1)

- ✔ Draw the new square with vertices: (-1, 2), (0, 2), (0, 1), (-1, 1)

> This places the square in the first quadrant, centered around ( -0.5, 1.5 )

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🔹 Bottom Left: Translate 3 units left

- Shape: A hexagon at (4, 2)
- Original coordinates (approximate):
- The hexagon appears symmetric around (4, 2). Its vertices are roughly:
- (3, 1), (3, 3), (4, 4), (5, 3), (5, 1), (4, 0)

- Translation: Move 3 units left → Subtract 3 from each x-coordinate

New coordinates:
- (3 - 3, 1) = (0, 1)
- (3 - 3, 3) = (0, 3)
- (4 - 3, 4) = (1, 4)
- (5 - 3, 3) = (2, 3)
- (5 - 3, 1) = (2, 1)
- (4 - 3, 0) = (1, 0)

- ✔ Draw the new hexagon with these points.

> This shifts the hexagon from the right side to the center of the grid.

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🔹 Bottom Right: Translate 4 right and 3 down

- Shape: An "L"-shaped figure
- Original coordinates:
- It consists of 5 squares:
- (-4, 4), (-3, 4), (-2, 4)
- (-4, 3), (-4, 2)

- Translation: 4 right → +4 to x; 3 down → -3 to y

New coordinates:
- (-4 + 4, 4 - 3) = (0, 1)
- (-3 + 4, 4 - 3) = (1, 1)
- (-2 + 4, 4 - 3) = (2, 1)
- (-4 + 4, 3 - 3) = (0, 0)
- (-4 + 4, 2 - 3) = (0, -1)

- ✔ Draw the new L-shape with these points:
- (0,1), (1,1), (2,1), (0,0), (0,-1)

> This moves the shape to the right and downward, placing it near the origin.

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✔ Summary of Translations:

| Problem | Original Shape | Direction | New Position |
|--------|----------------|----------|--------------|
| Top Left | Triangle | 4 right | From (-4,-4) area to (0,-4) area |
| Top Right | Square | 3 right, 2 down | From (-4,4) to (-1,2) |
| Bottom Left | Hexagon | 3 left | From (4,2) area to (1,2) area |
| Bottom Right | L-shape | 4 right, 3 down | From (-4,4) to (0,1) |

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📝 How to Solve These:

1. Identify the coordinates of all key points (vertices) of the shape.
2. Apply the translation:
- Right: Add to x
- Left: Subtract from x
- Up: Add to y
- Down: Subtract from y
3. Plot the new points and draw the translated shape.

> Remember: Translations do not change the size or orientation — only position.

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Let me know if you'd like a visual sketch or coordinate table for any specific one!