# Rotational Transformation

## Rotation Transformation - How It Works - Video

### Notation of the Points

Notation

These are the notations on how to transform the coordinate points on shapes or figures on a coordinate grid.

Going 90° clockwise or one quarter turn to the right is the same as going 270° counterclockwise or 3 quarter turns to the left ==> (x, y) => (y , -x). For example, (4, 2) becomes (2, -4).

Going 180° clockwise or two quarter turns to the right is the same as going 180° counterclockwise or 2 quarter turns to the left ==> (x, y) => (-x , -y). For example, (4, 2) becomes (-4, -2).

Going 270° clockwise or three quarter turns to the right is the same as going 90° counterclockwise or 1 quarter turn to the left ==> (x, y) => (-y , x). For example, (4, 2) becomes (-2, 4).

### Example 1

Example 1:

The pre-image is where the image originally. The image is where the image has been transformed to. Since we are rotating the image 90° clockwise, we move one quarter turn or one quadrant to the right. If we connect the vertices to the origin, where we are rotating around, the angle that is formed between the dotted lines is 90°.

The red dotted lines, the purple dotted lines, and the green dotted lines are form 90° angles. Just like the question asks.

Example 1 continued:

Since we are rotating 90° clockwise, we are going to use the notation of (x, y) => (y, -x) to transform the points to the correct spot.

• A: (1, 1) becomes A': (1, -1).

• B: (1, 4) becomes B': (4, -1).

• C: (2, 4) becomes C': (4, -2).

• D: (2, 3) becomes E': (3, -2).

• E: (4, 3) becomes D': (3, -4).

• F: (4, 1) becomes F': (1, -4).

If the questioned had asked to rotate the image 270° counterclockwise, we would get the same answer.

### Example 2

Example 2:

The pre-image is where the image originally. The image is where the image has been transformed to. Since we are rotating the image 90° counterclockwise, we move one quarter turn or one quadrant to the left. If we connect the vertices to the origin, where we are rotating around, the angle that is formed between the dotted lines is 90°.

The red dotted lines, the purple dotted lines, and the green dotted lines are form 90° angles. Just like the question asks.

Example 2 continued:

Since we are rotating 90° counterclockwise, we are going to use the notation of (x, y) => (-y, x) to transform the points to the correct spot.

• A: (1, 1) becomes A': (-1, 1).

• B: (1, 4) becomes B': (-4, 1).

• C: (2, 4) becomes C': (-4, 2).

• D: (2, 3) becomes E': (-3, 2).

• E: (4, 3) becomes D': (-3, 4).

• F: (4, 1) becomes F': (-1, 4).

If the questioned had asked to rotate the image 90° clockwise, we would get the same answer.

### Example 3

Example 3:

The pre-image is where the image originally. The image is where the image has been transformed to. Since we are rotating the image 180° clockwise, we move two quarter turns or two quadrants to the right. If we connect the vertices to the origin, where we are rotating around, the angle that is formed between the dotted lines is 180°.

The red dotted lines, the purple dotted lines, and the green dotted lines are form 180° angles. Just like the question asks.

Example 3 continued:

Since we are rotating 180° clockwise, we are going to use the notation of (x, y) => (-x, -y) to transform the points to the correct spot.

• A: (1, 1) becomes A': (-1, -1).

• B: (1, 4) becomes B': (-1, -4).

• C: (2, 4) becomes C': (-2, -4).

• D: (2, 3) becomes E': (-2, -3).

• E: (4, 3) becomes D': (-4, -3).

• F: (4, 1) becomes F': (-4, -1).

If the questioned had asked to rotate the image 180° counterclockwise, we would get the same answer.