1. Rotation 180° clockwise about the origin 3 A D 1 J - X

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**Rotation 180° Clockwise About the Origin**

To understand the concept of rotating a shape 180° clockwise about the origin, consider the diagram provided. 

The diagram features four quadrants with the origin (0,0) at the central intersection of the x-axis and y-axis. The figure in the diagram is a quadrilateral labeled with points A, B, C, and D. The rotation is centered at the origin, as indicated by the coordinate axes.

Key steps of the process:

1. **Identification of original points**: Identify the coordinates of each vertex of the quadrilateral. Let’s assume the coordinates are as follows for simplicity:
    - Point A (a, b)
    - Point B (c, d)
    - Point C (e, f)
    - Point D (g, h)

2. **Applying the rotation rule for 180° clockwise**: When rotating a point 180° clockwise about the origin:
    - The new coordinates will be (-x, -y) for each point (x, y).

3. **Calculating the new points**: Apply the rotation to each point:
    - Point A' (-a, -b)
    - Point B' (-c, -d)
    - Point C' (-e, -f)
    - Point D' (-g, -h)

4. **Plotting the new points**: Plot these new coordinates on the same graph to visualize the rotated quadrilateral.

The resulting shape will be a reflection of the original quadrilateral across both the x-axis and y-axis. The shape’s orientation remains similar, but its position will be inverted relative to the origin.

**Illustration**:

- Original coordinates: 
    - Point A is on the second quadrant.
    - Point B is on the first quadrant.
    - Point C is on the fourth quadrant.
    - Point D is on the third quadrant.

After rotating 180° clockwise, each point will be as follows:

- A shifts to the fourth quadrant.
- B shifts to the third quadrant.
- C shifts to the second quadrant.
- D shifts to the first quadrant.

This type of transformation is important in geometry and helps in understanding symmetrical properties and spatial reasoning.
Transcribed Image Text:**Rotation 180° Clockwise About the Origin** To understand the concept of rotating a shape 180° clockwise about the origin, consider the diagram provided. The diagram features four quadrants with the origin (0,0) at the central intersection of the x-axis and y-axis. The figure in the diagram is a quadrilateral labeled with points A, B, C, and D. The rotation is centered at the origin, as indicated by the coordinate axes. Key steps of the process: 1. **Identification of original points**: Identify the coordinates of each vertex of the quadrilateral. Let’s assume the coordinates are as follows for simplicity: - Point A (a, b) - Point B (c, d) - Point C (e, f) - Point D (g, h) 2. **Applying the rotation rule for 180° clockwise**: When rotating a point 180° clockwise about the origin: - The new coordinates will be (-x, -y) for each point (x, y). 3. **Calculating the new points**: Apply the rotation to each point: - Point A' (-a, -b) - Point B' (-c, -d) - Point C' (-e, -f) - Point D' (-g, -h) 4. **Plotting the new points**: Plot these new coordinates on the same graph to visualize the rotated quadrilateral. The resulting shape will be a reflection of the original quadrilateral across both the x-axis and y-axis. The shape’s orientation remains similar, but its position will be inverted relative to the origin. **Illustration**: - Original coordinates: - Point A is on the second quadrant. - Point B is on the first quadrant. - Point C is on the fourth quadrant. - Point D is on the third quadrant. After rotating 180° clockwise, each point will be as follows: - A shifts to the fourth quadrant. - B shifts to the third quadrant. - C shifts to the second quadrant. - D shifts to the first quadrant. This type of transformation is important in geometry and helps in understanding symmetrical properties and spatial reasoning.
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