Translation Worksheets - Free Printable

To solve the problems involving the translation of a point on a coordinate grid, we need to follow these steps:

1. Identify the starting coordinates of the point: Locate the initial position of the point on the grid.
2. Understand the translation instructions: Determine how many units to move horizontally (left or right) and vertically (up or down).
3. Apply the translation:
- Moving right increases the x-coordinate.
- Moving left decreases the x-coordinate.
- Moving up increases the y-coordinate.
- Moving down decreases the y-coordinate.
4. Plot the new coordinates: Mark the new position of the point on the grid.

Let's go through each problem step by step using an example from the image.

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Example Problem:

#### Problem 1: "Start at (3, 2). Move 2 units right and 1 unit up."

1. Starting Coordinates: The point starts at (3, 2).
2. Translation Instructions:
- Move 2 units right: This means adding 2 to the x-coordinate.
- Move 1 unit up: This means adding 1 to the y-coordinate.
3. New Coordinates:
- New x-coordinate: \(3 + 2 = 5\)
- New y-coordinate: \(2 + 1 = 3\)
- Therefore, the new coordinates are \((5, 3)\).
4. Plot the Point: Mark the point at \((5, 3)\) on the grid.

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General Steps for All Problems:

For each problem, follow these steps:
1. Identify the starting coordinates.
2. Apply the horizontal translation (right or left).
3. Apply the vertical translation (up or down).
4. Plot the new coordinates on the grid.

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Solution for Each Problem:

Here are the solutions for all the problems in the image. I'll summarize them below:

#### Problem 1: Start at (3, 2). Move 2 units right and 1 unit up.
- Starting: (3, 2)
- Translation: Right 2, Up 1
- New Coordinates: \((3 + 2, 2 + 1) = (5, 3)\)

#### Problem 2: Start at (1, 4). Move 3 units left and 2 units down.
- Starting: (1, 4)
- Translation: Left 3, Down 2
- New Coordinates: \((1 - 3, 4 - 2) = (-2, 2)\)

#### Problem 3: Start at (5, 1). Move 1 unit left and 3 units up.
- Starting: (5, 1)
- Translation: Left 1, Up 3
- New Coordinates: \((5 - 1, 1 + 3) = (4, 4)\)

#### Problem 4: Start at (2, 3). Move 4 units right and 1 unit down.
- Starting: (2, 3)
- Translation: Right 4, Down 1
- New Coordinates: \((2 + 4, 3 - 1) = (6, 2)\)

#### Problem 5: Start at (4, 5). Move 2 units left and 2 units up.
- Starting: (4, 5)
- Translation: Left 2, Up 2
- New Coordinates: \((4 - 2, 5 + 2) = (2, 7)\)

#### Problem 6: Start at (0, 0). Move 3 units right and 3 units up.
- Starting: (0, 0)
- Translation: Right 3, Up 3
- New Coordinates: \((0 + 3, 0 + 3) = (3, 3)\)

#### Problem 7: Start at (6, 2). Move 1 unit left and 4 units down.
- Starting: (6, 2)
- Translation: Left 1, Down 4
- New Coordinates: \((6 - 1, 2 - 4) = (5, -2)\)

#### Problem 8: Start at (3, 5). Move 2 units right and 3 units down.
- Starting: (3, 5)
- Translation: Right 2, Down 3
- New Coordinates: \((3 + 2, 5 - 3) = (5, 2)\)

#### Problem 9: Start at (1, 1). Move 4 units right and 2 units up.
- Starting: (1, 1)
- Translation: Right 4, Up 2
- New Coordinates: \((1 + 4, 1 + 2) = (5, 3)\)

#### Problem 10: Start at (5, 3). Move 3 units left and 1 unit down.
- Starting: (5, 3)
- Translation: Left 3, Down 1
- New Coordinates: \((5 - 3, 3 - 1) = (2, 2)\)

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Final Answer:

The new coordinates for each problem are:
1. \((5, 3)\)
2. \((-2, 2)\)
3. \((4, 4)\)
4. \((6, 2)\)
5. \((2, 7)\)
6. \((3, 3)\)
7. \((5, -2)\)
8. \((5, 2)\)
9. \((5, 3)\)
10. \((2, 2)\)

\[
\boxed{(5, 3), (-2, 2), (4, 4), (6, 2), (2, 7), (3, 3), (5, -2), (5, 2), (5, 3), (2, 2)}
\]