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Rotations review

Review the basics of rotations, and then perform some rotations.

What is a rotation?

A rotation is a type of transformation that takes each point in a figure and rotates it a certain number of degrees around a given point.
For example, this animation shows a rotation of pentagon I, D, E, A, L about the point left parenthesis, 0, comma, minus, 1, right parenthesis. You can see the angle of rotation at the bottom, which increases the further we rotate the figure from its original position.
The result of a rotation is a new figure, called the image. The image is congruent to the original figure.
Want to learn more about different types of transformations? Check out this video.

Performing rotations

Although a figure can be rotated any number of degrees, the rotation will usually be a common angle such as 45, degreesor 180, degrees.
If the number of degrees are positive, the figure will rotate counter-clockwise.
If the number of degrees are negative, the figure will rotate clockwise.
The figure can rotate around any given point.
Example:
Rotate triangle, O, A, R 60, degrees about point left parenthesis, minus, 2, comma, minus, 3, right parenthesis.
The center of rotation is left parenthesis, minus, 2, comma, minus, 3, right parenthesis.
Rotation by 60, degrees moves each point about left parenthesis, minus, 2, comma, minus, 3, right parenthesis in a counter-clockwise direction. The rotation maps triangle, O, A, R onto the triangle below.
Want to learn more about performing rotations? Check out this video.

Practice

Problem 1
triangle, N, O, W is rotated 90, degrees about the origin.
Draw the image of this rotation.

Want to try more problems like this? Check out this exercise.

Want to join the conversation?

  • female robot grace style avatar for user Alisa Zhupanenko
    Why is positive counter-clockwise? Is that just a rule or...
    (38 votes)
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    • leaf blue style avatar for user Nickerson, Logan Nickerson
      I know the exact story very well: One time zeus was walking in the garden, and he stepped on a rat and screamed. Not wanting to be seen as a wimp, he killed his brother/mom hermes. An imp though it wasnt very nice so he was turned into a mosquito. Then hypotenuse the mathematician told zeus that his chin was a 90 degree angle, which he enjoyed. Now, at the time, hypotenuse hated the fromaguebaguette dance, which consisted of clockwise spinning. His wife died dancing clockwise. So he asked zeus a simple request: to make positive (good) of the counterclockwise. And zeus said yes, but that hypotenuse might regret his choice. And soon enough, hypotenuse was killed by a confused teenager trying to math-ize counterclockwise. Zeus sighed, and then made negative rotation a thing to keep any more Greek mathematicians from dying. So that is how it happened.
      (5 votes)
  • starky ultimate style avatar for user Si̶ℓvεɾ Wølƒ
    So how do you suppose the exact rotation on here? Or do you just guess how much to turn it ....
    (19 votes)
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  • blobby green style avatar for user Kayla  Brown
    I have to find the coordinates of a point on a shape after a rotation, but I wasn't given a graph or any image.
    (Example):'triangle'NPQ has vertices N(-6,-4), P(-3,4), and Q(1,1). If the triangle is rotated 90 degrees about the origin, what are the coordinates of P'?
    Is there a rule or formula to solve this or do I have to actually draw a graph, plot the points, rotate, ect.? Thanks.
    (9 votes)
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  • piceratops ultimate style avatar for user Jessica
    I don't understand how to rotate about the origin, please explain.
    (2 votes)
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    • male robot johnny style avatar for user Jeremy Quilter
      @garrettcummings22, I realize the frustration of these geometric principles, but these same principles are the foundations of graphic design, several types of engineering, carpentry, masonry, many forms of art. The reality is no one in grades 7-12 will ever know if they will use any of the math they are required to study. No one knows what their future holds. Reality also tells us that every math principle taught is a math concept actually used somewhere in real life. I have used several concepts, especially writing, solving, and graphing linear equations, Pythagorean Theorem, ratios and percents, and many other aspects of statistics throughout my many years of life and many occupations in life.

      Good luck in all you do. I hope you find some purpose in your life for the math. I genuinely mean that.
      (2 votes)
  • blobby green style avatar for user gamilah.alrabuoi@uascjstudent.org
    what way counter-clockwise go and what way does clockwise go.
    (3 votes)
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  • starky sapling style avatar for user _DEMARION_🦄👻😺👹
    I think this lesson is better taught without the computer.So if you don't understand try it on 8th grade lesson 7 with the eureka math book :)
    (6 votes)
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  • starky seed style avatar for user Mathew Jilton
    Math really do be makin' me educated
    (4 votes)
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  • blobby green style avatar for user mea883
    I put the rotating point at 0,0 and it said I was wrong. But the explanation had the rotating point at 0,0.
    (4 votes)
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  • duskpin seedling style avatar for user Maddy
    Can someone explain how to write the rules for rotation?
    (4 votes)
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  • blobby green style avatar for user sjanke06
    I'm confuse about rotation.
    (3 votes)
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