Videos, worksheets, stories and songs to help Grade 7 students learn about rotation in geometry.

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More lessons on Rotation and other forms of Transformation

Transformation Games and Activities

### Rotation

A rotation (or turn) is a transformation that turns a line or a shape around a fixed point. This point is called the center of rotation. We usually measure the number of degrees of rotation of a shape in a counterclockwise direction.

**Introduction to Rotation**

Rotate 90 degrees clockwise

Rotate 90 degrees counterclockwise

Rotate 180 degrees**Math Rotations**

Students learn that when a figure is turned to a new position, the transformation is called a rotation.

Estimate the number of degrees and state the direction in which the following figure has been rotated.**Rotation of figures**

A video showing how to rotate a figure "x" degrees around a point.

How to rotate a figure 90 degrees rotation about a point O using a compass and a protractor.**Geometry Construction: Rotating a Figure by Hand**

How to rotate a figure around a fixed point using a compass and protractor.

Rotate "H" 100 degrees counterclockwise around a point P.

### Rotations on the Coordinate Plane

**Transformations - Rotate 90 degrees**

Rotating a polygon clockwise 90 degrees around the origin.

Step 1: For a 90 degree rotation around the origin, switch the x, y values of each ordered pair for the location of the new point.

Step 2: After you have your new ordered pairs, plot each point.**Rotate 180 Degrees Around The Origin**

This tutorial shows why all signs of an ordered pair of an object become opposite when rotating that object 180 degrees around the origin.**A lesson on transformations, with a focus on rotation and reflection**
**Rules for reflections and rotations on the coordinate plane**

**Common Rules of Reflection**

• Over x-axis: Keep x, change y i.e. (x,y) → (x,-y)

• Over y-axis: Change x, keep y i.e. (x,y) → (x,-y)

• Through origin: Change x, change y i.e. (x,y) → (-x,-y)

• Over the line y = x: Swap x and y i.e. (x,y) → (y,x)

• Over the line y = -x: Swap x and negate i.e. (x,y) → (-y,-x)

**Less Common Reflections**

To reflect over any line (or point):

- Plot given figure and given line (or point)

- Make a "path" from figure to line (or point)

- Repeat the same "path" to he image.

**Common Rules for Rotation**

• Rotation of 90°: (x,y) → (-y,x)

• Rotation of 180°: reflect through origin i.e. (x,y) → (-x,-y)

• Rotation of 270°: (x,y) → (y,-x)

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

Related Topics:

More lessons on Rotation and other forms of Transformation

Transformation Games and Activities

Rotate 90 degrees clockwise

Rotate 90 degrees counterclockwise

Rotate 180 degrees

Students learn that when a figure is turned to a new position, the transformation is called a rotation.

Estimate the number of degrees and state the direction in which the following figure has been rotated.

A video showing how to rotate a figure "x" degrees around a point.

How to rotate a figure 90 degrees rotation about a point O using a compass and a protractor.

How to rotate a figure around a fixed point using a compass and protractor.

Rotate "H" 100 degrees counterclockwise around a point P.

Rotating a polygon clockwise 90 degrees around the origin.

Step 1: For a 90 degree rotation around the origin, switch the x, y values of each ordered pair for the location of the new point.

Step 2: After you have your new ordered pairs, plot each point.

This tutorial shows why all signs of an ordered pair of an object become opposite when rotating that object 180 degrees around the origin.

• Over x-axis: Keep x, change y i.e. (x,y) → (x,-y)

• Over y-axis: Change x, keep y i.e. (x,y) → (x,-y)

• Through origin: Change x, change y i.e. (x,y) → (-x,-y)

• Over the line y = x: Swap x and y i.e. (x,y) → (y,x)

• Over the line y = -x: Swap x and negate i.e. (x,y) → (-y,-x)

To reflect over any line (or point):

- Plot given figure and given line (or point)

- Make a "path" from figure to line (or point)

- Repeat the same "path" to he image.

• Rotation of 90°: (x,y) → (-y,x)

• Rotation of 180°: reflect through origin i.e. (x,y) → (-x,-y)

• Rotation of 270°: (x,y) → (y,-x)

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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