Four geometry problems asking students to translate shapes like trapezoids and triangles in different directions on a grid.

The task involves translating geometric shapes on a grid according to specific instructions. Translation means moving the shape to a new position without rotating or flipping it. Here's how to solve each part step by step:

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1) Translate this shape 4 spaces to the right.

- Shape: A trapezoid.
- Instructions: Move the shape 4 spaces to the right.

#### Steps:
1. Identify the coordinates of the vertices of the trapezoid.
2. Add 4 to the x-coordinate of each vertex (since we are moving right).
3. Plot the new vertices and draw the translated shape.

#### Solution:
- The original trapezoid is positioned such that its leftmost vertex is at, say, \((x_1, y_1)\). Moving it 4 spaces to the right means shifting all vertices by \(+4\) in the x-direction.
- The new trapezoid will be drawn with all its vertices shifted 4 units to the right.

Final Answer for 1:

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2) Translate this shape 3 spaces to the left.

- Shape: A right triangle.
- Instructions: Move the shape 3 spaces to the left.

#### Steps:
1. Identify the coordinates of the vertices of the triangle.
2. Subtract 3 from the x-coordinate of each vertex (since we are moving left).
3. Plot the new vertices and draw the translated shape.

#### Solution:
- The original triangle is positioned such that its rightmost vertex is at, say, \((x_1, y_1)\). Moving it 3 spaces to the left means shifting all vertices by \(-3\) in the x-direction.
- The new triangle will be drawn with all its vertices shifted 3 units to the left.

Final Answer for 2:

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3) Translate this shape 4 spaces down.

- Shape: A hexagon.
- Instructions: Move the shape 4 spaces down.

#### Steps:
1. Identify the coordinates of the vertices of the hexagon.
2. Subtract 4 from the y-coordinate of each vertex (since we are moving down).
3. Plot the new vertices and draw the translated shape.

#### Solution:
- The original hexagon is positioned such that its topmost vertex is at, say, \((x_1, y_1)\). Moving it 4 spaces down means shifting all vertices by \(-4\) in the y-direction.
- The new hexagon will be drawn with all its vertices shifted 4 units downward.

Final Answer for 3:

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4) Translate this shape 3 spaces up.

- Shape: An equilateral triangle.
- Instructions: Move the shape 3 spaces up.

#### Steps:
1. Identify the coordinates of the vertices of the triangle.
2. Add 3 to the y-coordinate of each vertex (since we are moving up).
3. Plot the new vertices and draw the translated shape.

#### Solution:
- The original triangle is positioned such that its bottommost vertex is at, say, \((x_1, y_1)\). Moving it 3 spaces up means shifting all vertices by \(+3\) in the y-direction.
- The new triangle will be drawn with all its vertices shifted 3 units upward.

Final Answer for 4:

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Summary of Final Answers:

1. The trapezoid is translated 4 spaces to the right.
2. The triangle is translated 3 spaces to the left.
3. The hexagon is translated 4 spaces down.
4. The equilateral triangle is translated 3 spaces up.

Boxed Final Answer:
\[
\boxed{
\text{See the translations in the images above.}
}
\]