QUICK LINKS


Rotations Calculator

QUICK LINKS


Rotations Calculator

CALCULATOR

Rotation Calculator

Step 1. Identify the center of rotation.

Step 2. Identify the original points.

How many points does your original have?
Enter the original points:
Original Points

Step 3. Subtract the center of rotation from each original point.

We're basically translating the shape to the origin so that we can use our rotation formulas.

Step 3. Identify the angle and direction of the rotation.

From the question, we know we are rotating the shape .
Direction:Angle of Rotation:

Step 4. Identify the formula that matches the rotation.

We have some questions for you! Help us out through this
INTRO
A rotation is a type of rigid transformation, which means it changes the position or orientation of an image without changing its size or shape.
A rotation does this by rotating an image a certain amount of degrees either clockwise ↻ or counterclockwise ↺.
For rotations of , , and in either direction around the origin , there are formulas we can use to figure out the new points of an image after it has been rotated.
Clockwise ↻Counterclockwise ↺
When we simplify, we can see that the counterclockwise and clockwise rotations are just the reverse of each other. So there are really only 3 rotation formulas we need to remember.
To help us understand and remember the rotation formulas, we like to imagine two arrows rotating.
The arrows start pointing in the positive and directions. As they rotate, we use their new positions to determine the changes in and .
Remember, there are in a circle, which means that each quarter turn is .
Try rotating different points around the origin:
Point:Direction:Angle of Rotation:
Check out our
Calculator
or explore our
Lesson
and
Practice
sections to learn more about rotations and test your understanding.

You can also use the Quick Links menu on the left to jump to a section of your choice.

You can also use the Quick Links dropdown above to jump to a section of your choice.

KEY STEPS

How to Perform Rotations

Step 1. Identify the center of rotation.

Step 2. Identify the original points.

Step 3. Identify the angle and direction of rotation.

Direction:Angle of Rotation:

Step 4. Identify the formula that matches the rotation.

When we rotate counterclockwise:
  • The axis lines up with the arrow pointing in the negative direction, so the new value is the negative of the old value.
  • The axis lines up with the arrow pointing in the positive direction, so the new value is the old value.

Step 5. Apply the formula to each original point to get the new points.

Original PointNew Point
......

Step 6. Plot the new points.

LESSON
Rotations around the Origin
PRACTICE
Rotations around the Origin
LESSON
Rotations NOT around the Origin
PRACTICE
Rotations NOT around the Origin
CONCLUSION
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