Table of Contents

- 1 How do you determine rotation?
- 2 How do you describe a rotation in math?
- 3 What are the properties that identify a rotation?
- 4 How do you perform a rotation we must specify?
- 5 What are the properties of rotations?
- 6 What information is needed to properly rotate a figure?
- 7 Do rotations commute?
- 8 Which are not changed after a rotation?
- 9 What do you need to know about geometry rotation?
- 10 What happens when the coordinates of an image are rotated?

## How do you determine rotation?

The point of rotation is the origin, draw lines joining one of the points, say X and it’s image to the origin. You can see that the lines form an angle of 270° , in the counterclockwise direction. Therefore, ΔX’Y’Z’ is obtained by rotating ΔXYZ counterclockwise by 270° about the origin.

## How do you describe a rotation in math?

Rotation turns a shape around a fixed point called the centre of rotation. Rotation is an example of a transformation. A transformation is a way of changing the size or position of a shape. The shape has been rotated 90° (a quarter turn) clockwise about the centre of rotation.

**Why don’t you need to know the direction of rotation when the angle of rotation is 180 degrees?**

“What information do you need to do a rotation?” (Center, angle, and direction of rotation.) “Why don’t you need to know the direction of rotation when the angle of rotation is 180 degrees?” (Both clockwise and counterclockwise land in the same place since 180 degrees is half a circle.)

### What are the properties that identify a rotation?

The following are the three basic properties of rotations :

- A rotation maps a line to a line, a ray to a ray, a segment to a segment, and an angle to an angle.
- A rotation preserves lengths of segments.
- A rotation preserves measures of angles.

### How do you perform a rotation we must specify?

Explanation: Generate a rotation, we must specify rotation angle ϴ of the rotation point or pivot point which the object is to be rotated. Explanation: A positive value for the rotation angle ϴ defines counterclockwise rotations about the pivot point.

**When describing a rotation What information must you include?**

A rotation is described by the centre of rotation, the angle of rotation, and the direction of the turn. The centre of rotation is the point that a shape rotates around. Each point in the shape must stay an equal distance from the centre of rotation.

## What are the properties of rotations?

## What information is needed to properly rotate a figure?

To describe a rotation, you need three things:

- Direction (clockwise CW or counterclockwise CCW)
- Angle in degrees.
- Center point of rotation (turn about what point?)

**What are the rules for clockwise rotations?**

Here are the rotation rules:

- 90° clockwise rotation: (x,y) becomes (y,-x)
- 90° counterclockwise rotation: (x,y) becomes (y,x)
- 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)
- 270° clockwise rotation: (x,y) becomes (-y,x)
- 270° counterclockwise rotation: (x,y) becomes (y,-x)

### Do rotations commute?

Rotations about different points, in general, do not commute. Any two-dimensional direct motion is either a translation or a rotation; see Euclidean plane isometry for details.

### Which are not changed after a rotation?

Line segments connecting the center of rotation to a point on the pre-image and the corresponding point on the image have equal length. The line segments connecting corresponding vertices are not parallel. Which are not changed after a rotation? No, the vertices of the image and pre-image do not correspond.

**Which is the correct description of a rotation?**

A rotation is a transformation in which the object is rotated about a fixed point. The direction of rotation can be clockwise or anticlockwise. The fixed point in which the rotation takes place is called the center of rotation . The amount of rotation made is called the angle of rotation.

## What do you need to know about geometry rotation?

Geometry Rotation A rotation is an isometric transformation: the original figure and the image are congruent. The orientation of the image also stays the same, unlike reflections. To perform a geometry rotation, we first need to know the point of rotation, the angle of rotation,…

## What happens when the coordinates of an image are rotated?

It will be helpful to note the patterns of the coordinates when the points are rotated about the origin at different angles. A rotation is an isometric transformation: the original figure and the image are congruent. The orientation of the image also stays the same, unlike reflections.

**How are the orientation and position of an object represented?**

Rotations and Orientation. Position and Orientation. The position of an object can be represented as a translation of the object from the origin The orientation of an object can be represented as a rotation of an object from its original unrotated orientation.