📚 Practice With Worksheets
Extend your learning by practicing rotations about the origin and analyzing how coordinates change after 90° and 180° rotations.
▶️ Learn With Videos
Watch these lessons to learn how figures rotate around the origin by 90° and 180° and how coordinates change after each rotation.
🛠️ How to Use This Tool
Drag the vertices of the figure to create your own shape. You can also drag the center of rotation or enter coordinates for a new center.
Use the buttons to rotate the figure \(90^\circ\) clockwise, \(90^\circ\) counterclockwise, or \(180^\circ\). Watch how the coordinates change after each transformation.
Compare the original figure to the rotated image. Notice that rotations preserve size and shape even though the orientation and coordinates change.
🧠 Things to Think About
Why is a \(90^\circ\) rotation called a quarter turn? Why is a \(180^\circ\) rotation called a half turn?
How do the coordinates change when a figure rotates around the origin? What patterns do you notice after several rotations?
Can a rotation change the size or shape of a figure? Why or why not? How many \(90^\circ\) rotations would return a figure to its original position?
📘 Vocabulary & Rotation Rules
Transformation: A change in the position, size, or orientation of a figure.
Rotation: A transformation that turns a figure around a fixed point.
Center of Rotation: The fixed point around which the figure rotates.
Origin: The point \((0,0)\) on the coordinate plane.
Rigid Transformation: A transformation that preserves size and shape.
Congruent Figures: Figures that have the same size and shape.
Clockwise Rotation: A turn in the same direction as the hands of a clock.
Counterclockwise Rotation: A turn opposite the direction of a clock's hands.
\(90^\circ\) Counterclockwise About the Origin:
\((x,y)\rightarrow(-y,x)\)
\(90^\circ\) Clockwise About the Origin:
\((x,y)\rightarrow(y,-x)\)
\(180^\circ\) Rotation About the Origin:
\((x,y)\rightarrow(-x,-y)\)
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