## Key Concept

- Rotation
- Rotations in a coordinate plane
- Describe rotation

**Rotation**

The rotation occurs when we turn around a given point. We can define rotation as a transformation around a fixed point called the centre of rotation.

Rotations can occur either clockwise or anti-clockwise.

The figure does not change the size.

The point (x, y) in different quadrants in the x y plane or coordinate plane.

**Understanding Rotations**

### Rotation in different quadrants in a coordinate plane

Let the image be in the first quadrant

- If the image is moving in an anti-clockwise direction at 90°, it will move to the second quadrant, and if the image is moving in a clockwise direction at 90°, the image will move to the fourth quadrant.

- If the image is moving 180°, it will move to the third quadrant in both clockwise and anti-clockwise directions.
- If the image is moving in an anti-clockwise direction at 270°, it will move to the fourth quadrant, and if the image is moving clockwise direction 270°, the image will move to the second quadrant.
- The rotation of 360° would match the image with its preimage.

### Rules of rotation in different quadrants in a coordinate plane in both clockwise and counter-clockwise directions.

**Rotations in the coordinate plane about the origin **

Coordinates of the point after transformation or rotation of 90° and 180° around the origin.

**Example 1**

Rotation of 90° counter-clockwise about the origin

**Example 2**

Rotation of 180° about the origin

**Example 3**

**Coordinates of the point after transformation or rotation**

**V’(3, 2), E’(-2, 1), G’(0, 3)**

**Example 4**

**Coordinates of the point after transformation or rotation**

**A’(3, 3), B(7, –5), C(10, –10)**

**What did we discuss in this session?**

Based on the figure, answer the following:

Points are R(1, 3), S(4, 4), T(2, 1)

If the image is moving 90° clockwise, what will be the coordinates of R’S’T’?

The points are R’ (3, -1), S’(4, -4), T’(1, -4)

If the image is moving 90° counter-clockwise, what will be the coordinate of R’S’T’?

The points are R’ (-3, 1), S’(-4, 4), T’(4, 1)

If the image is moving 180° clockwise, what will be the coordinates of R’S’T’?

The points are R’(-1, -3), S’(-4, -4), T’(-2, -1)

If the image is moving 180° counter-clockwise, what will be the coordinates of R’S’T’?

The points are R’(-1, -3), S’(-4, -4), T’(-2, -1)

If the image is moving 270° counter-clockwise, what will be the coordinates of R’S’T’?

## Exercise:

- 1. Why rotation is called a rigid transformation?
- 2. In what quadrant will an image be if a figure is in quadrant II and is rotated 90° clockwise?
- 3. In what quadrant will an image be if a figure is in quadrant III and is rotated 180° clockwise?
- 4. In what quadrant will an image be if a figure is in quadrant I and is rotated 90° counterclockwise?
- 5. Rotate the figure 90° counter-clockwise and write the coordinates.

6. Rotate the figure 180° clockwise and write the coordinates.

The points are R’ (-3, 1), S’(-4, 4), T’(4, 1)

**Concept Map**

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