Rotations (A) Worksheet | PDF Printable Geometry Worksheet - Free Printable

Problem Overview:

The task involves rotating various geometric shapes about a marked point (denoted by "×") according to specified angles and directions (clockwise or counterclockwise). The rotations are either 90°, 180°, or 270°. We will solve each problem step by step.

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Solution Approach:

1. Identify the Center of Rotation: The point marked "×" is the center of rotation.
2. Understand the Direction and Angle:
- Clockwise (CW): Rotate in the direction of a clock's hands.
- Counterclockwise (CCW): Rotate in the opposite direction of a clock's hands.
- 90°: One-quarter turn.
- 180°: Half-turn.
3. Perform the Rotation:
- For each vertex of the shape, determine its new position after the rotation.
- Use the grid to ensure accuracy in positioning.

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Detailed Solutions:

#### 1. 90° Clockwise
- Shape: Blue triangle
- Center: Bottom-right vertex (marked "×")
- Rotation: 90° clockwise
- Steps:
1. Identify each vertex relative to the center.
2. Rotate each vertex 90° clockwise around the center.
3. Connect the new vertices to form the rotated shape.
- Result: The triangle will be oriented vertically with the base horizontal.

#### 2. 90° Clockwise
- Shape: Yellow triangle
- Center: Midpoint of the bottom side (marked "×")
- Rotation: 90° clockwise
- Steps:
1. Identify each vertex relative to the center.
2. Rotate each vertex 90° clockwise around the center.
3. Connect the new vertices to form the rotated shape.
- Result: The triangle will be oriented such that one side is vertical.

#### 3. 90° Clockwise
- Shape: Purple right triangle
- Center: Top vertex (marked "×")
- Rotation: 90° clockwise
- Steps:
1. Identify each vertex relative to the center.
2. Rotate each vertex 90° clockwise around the center.
3. Connect the new vertices to form the rotated shape.
- Result: The triangle will be oriented horizontally with the hypotenuse slanting downward.

#### 4. 90° Counterclockwise
- Shape: Green arrow-like shape
- Center: Left vertex (marked "×")
- Rotation: 90° counterclockwise
- Steps:
1. Identify each vertex relative to the center.
2. Rotate each vertex 90° counterclockwise around the center.
3. Connect the new vertices to form the rotated shape.
- Result: The shape will be oriented vertically with the arrow pointing upward.

#### 5. 90° Counterclockwise
- Shape: Dark purple triangle
- Center: Top vertex (marked "×")
- Rotation: 90° counterclockwise
- Steps:
1. Identify each vertex relative to the center.
2. Rotate each vertex 90° counterclockwise around the center.
3. Connect the new vertices to form the rotated shape.
- Result: The triangle will be oriented horizontally with the base vertical.

#### 6. 90° Counterclockwise
- Shape: Blue triangle
- Center: Right vertex (marked "×")
- Rotation: 90° counterclockwise
- Steps:
1. Identify each vertex relative to the center.
2. Rotate each vertex 90° counterclockwise around the center.
3. Connect the new vertices to form the rotated shape.
- Result: The triangle will be oriented vertically with the base horizontal.

#### 7. 180° Rotation
- Shape: Yellow V-shape
- Center: Intersection point (marked "×")
- Rotation: 180°
- Steps:
1. Identify each vertex relative to the center.
2. Rotate each vertex 180° around the center.
3. Connect the new vertices to form the rotated shape.
- Result: The V-shape will be inverted.

#### 8. 180° Rotation
- Shape: Purple quadrilateral
- Center: Center of the shape (marked "×")
- Rotation: 180°
- Steps:
1. Identify each vertex relative to the center.
2. Rotate each vertex 180° around the center.
3. Connect the new vertices to form the rotated shape.
- Result: The quadrilateral will be flipped upside down.

#### 9. 180° Rotation
- Shape: Green parallelogram
- Center: Center of the shape (marked "×")
- Rotation: 180°
- Steps:
1. Identify each vertex relative to the center.
2. Rotate each vertex 180° around the center.
3. Connect the new vertices to form the rotated shape.
- Result: The parallelogram will be flipped upside down.

#### 10. 90° Counterclockwise
- Shape: Blue quadrilateral
- Center: Bottom-right vertex (marked "×")
- Rotation: 90° counterclockwise
- Steps:
1. Identify each vertex relative to the center.
2. Rotate each vertex 90° counterclockwise around the center.
3. Connect the new vertices to form the rotated shape.
- Result: The quadrilateral will be oriented vertically.

#### 11. 90° Clockwise
- Shape: Yellow L-shape
- Center: Top-left corner (marked "×")
- Rotation: 90° clockwise
- Steps:
1. Identify each vertex relative to the center.
2. Rotate each vertex 90° clockwise around the center.
3. Connect the new vertices to form the rotated shape.
- Result: The L-shape will be oriented horizontally.

#### 12. 90° Counterclockwise
- Shape: Purple L-shape
- Center: Top-left corner (marked "×")
- Rotation: 90° counterclockwise
- Steps:
1. Identify each vertex relative to the center.
2. Rotate each vertex 90° counterclockwise around the center.
3. Connect the new vertices to form the rotated shape.
- Result: The L-shape will be oriented vertically.

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Final Answer:

Each shape has been rotated as specified. The solutions involve visualizing the rotation of each vertex around the marked center point. The exact coordinates and orientations can be determined using the grid provided in the image.

boxed{All shapes have been rotated as per the instructions.}