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More lessons on Rotation & other forms of Transformation

Transformation Games & Activities

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

The following diagram gives some rules of rotation. Scroll down the page for more examples and solutions.

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.

**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)

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