Geometry Worksheets | Transformations Worksheets - Free Printable

Problem Description:

The task involves performing translations of geometric shapes on a coordinate grid. Each translation is described by moving the shape a certain number of units horizontally (left or right) and/or vertically (up or down). The goal is to apply these translations accurately to the given shapes.

Solution Explanation:

#### Translation Basics:
- Right: Increase the x-coordinate by the specified number of units.
- Left: Decrease the x-coordinate by the specified number of units.
- Up: Increase the y-coordinate by the specified number of units.
- Down: Decrease the y-coordinate by the specified number of units.

We will apply each translation step-by-step to the given shapes.

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1) Translation: 3 right

- Original Shape: The shape is a triangle with vertices at approximately:
- \( A(−2, 1) \)
- \( B(−2, −1) \)
- \( C(0, −1) \)

- Translation: Move 3 units to the right.
- New coordinates:
- \( A'(−2 + 3, 1) = (1, 1) \)
- \( B'(−2 + 3, −1) = (1, −1) \)
- \( C'(0 + 3, −1) = (3, −1) \)

- Result: Draw the triangle with vertices at \( (1, 1) \), \( (1, −1) \), and \( (3, −1) \).

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2) Translation: 2 right and 3 down

- Original Shape: The shape is a quadrilateral with vertices at approximately:
- \( A(1, 4) \)
- \( B(3, 4) \)
- \( C(3, 2) \)
- \( D(1, 2) \)

- Translation: Move 2 units to the right and 3 units down.
- New coordinates:
- \( A'(1 + 2, 4 − 3) = (3, 1) \)
- \( B'(3 + 2, 4 − 3) = (5, 1) \)
- \( C'(3 + 2, 2 − 3) = (5, −1) \)
- \( D'(1 + 2, 2 − 3) = (3, −1) \)

- Result: Draw the quadrilateral with vertices at \( (3, 1) \), \( (5, 1) \), \( (5, −1) \), and \( (3, −1) \).

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3) Translation: 5 left

- Original Shape: The shape is a triangle with vertices at approximately:
- \( A(3, −2) \)
- \( B(5, −2) \)
- \( C(4, 0) \)

- Translation: Move 5 units to the left.
- New coordinates:
- \( A'(3 − 5, −2) = (−2, −2) \)
- \( B'(5 − 5, −2) = (0, −2) \)
- \( C'(4 − 5, 0) = (−1, 0) \)

- Result: Draw the triangle with vertices at \( (−2, −2) \), \( (0, −2) \), and \( (−1, 0) \).

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4) Translation: 4 left and 3 down

- Original Shape: The shape is an L-shaped figure with vertices at approximately:
- \( A(2, 2) \)
- \( B(2, 0) \)
- \( C(4, 0) \)
- \( D(4, −1) \)
- \( E(3, −1) \)

- Translation: Move 4 units to the left and 3 units down.
- New coordinates:
- \( A'(2 − 4, 2 − 3) = (−2, −1) \)
- \( B'(2 − 4, 0 − 3) = (−2, −3) \)
- \( C'(4 − 4, 0 − 3) = (0, −3) \)
- \( D'(4 − 4, −1 − 3) = (0, −4) \)
- \( E'(3 − 4, −1 − 3) = (−1, −4) \)

- Result: Draw the L-shaped figure with vertices at \( (−2, −1) \), \( (−2, −3) \), \( (0, −3) \), \( (0, −4) \), and \( (−1, −4) \).

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5) Translation: 4 left and 5 down

- Original Shape: The shape is an irregular polygon with vertices at approximately:
- \( A(1, 3) \)
- \( B(3, 3) \)
- \( C(3, 1) \)
- \( D(2, 1) \)
- \( E(2, 0) \)
- \( F(1, 0) \)

- Translation: Move 4 units to the left and 5 units down.
- New coordinates:
- \( A'(1 − 4, 3 − 5) = (−3, −2) \)
- \( B'(3 − 4, 3 − 5) = (−1, −2) \)
- \( C'(3 − 4, 1 − 5) = (−1, −4) \)
- \( D'(2 − 4, 1 − 5) = (−2, −4) \)
- \( E'(2 − 4, 0 − 5) = (−2, −5) \)
- \( F'(1 − 4, 0 − 5) = (−3, −5) \)

- Result: Draw the polygon with vertices at \( (−3, −2) \), \( (−1, −2) \), \( (−1, −4) \), \( (−2, −4) \), \( (−2, −5) \), and \( (−3, −5) \).

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6) Translation: 3 right and 4 up

- Original Shape: The shape is a triangle with vertices at approximately:
- \( A(−3, −2) \)
- \( B(−1, −2) \)
- \( C(−2, 0) \)

- Translation: Move 3 units to the right and 4 units up.
- New coordinates:
- \( A'(−3 + 3, −2 + 4) = (0, 2) \)
- \( B'(−1 + 3, −2 + 4) = (2, 2) \)
- \( C'(−2 + 3, 0 + 4) = (1, 4) \)

- Result: Draw the triangle with vertices at \( (0, 2) \), \( (2, 2) \), and \( (1, 4) \).

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Final Answer:

Each translation has been applied as described. The new positions of the shapes are determined by adjusting the coordinates according to the given instructions. The final answer is:

\[
\boxed{
\text{Translations applied as explained above.}
}
\]