Why is positive counter-clockwise? Is that just a rule or...

It’s because you’re rotating in the order of the coordinate plane’s quadrants, which goes from right to left to down to right (**counterclockwise**)

I don’t see how it’s possible to rotate any polygon free-hand,without the rotation tool.

You could rotate each point of the polygon *on its own*, and then connect each point correctly. Remember that each point will be the same distance from the centre of rotation.

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.

Great question! There are actually several helpful shortcuts for finding rotations. For rotating 90 degrees counterclockwise about the origin, a point (x, y) becomes (-y, x). So for example, your N would become (4, -6). For more information, try this link: https://uploads.desmos.com/activitybuilder/3deb2fa7414964f508e36f7de7bfd615

I don't understand how to rotate about the origin, please explain.

@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.

Main content

Course: 8th grade > Unit 6

Lesson 3: Rotations

Rotations review

Google Classroom

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

(0, - 1)

. 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^{\circ}

180^{\circ}

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

△ O A R

60^{\circ}

about point

(- 2, - 3)

The center of rotation is

(- 2, - 3)

Rotation by

60^{\circ}

moves each point about

(- 2, - 3)

in a counter-clockwise direction. The rotation maps

△ O A R

onto the triangle below.

Want to learn more about performing rotations? Check out this video.

Practice

Problem 1

△ N O W

is rotated

90^{\circ}

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?

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Alisa Zhupanenko
Posted 7 years ago. Direct link to Alisa Zhupanenko's post “Why is positive counter-c...”
Why is positive counter-clockwise? Is that just a rule or...
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(44 votes)
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- ngoc
  Posted 6 years ago. Direct link to ngoc's post “It’s because you’re rotat...”
  It’s because you’re rotating in the order of the coordinate plane’s quadrants, which goes from right to left to down to right (*counterclockwise*)
  Comment on ngoc's post “It’s because you’re rotat...”
  (16 votes)
Si̶ℓvεɾ Wølƒ
Posted 8 years ago. Direct link to Si̶ℓvεɾ Wølƒ's post “So how do you suppose the...”
So how do you suppose the exact rotation on here? Or do you just guess how much to turn it ....
Button navigates to signup pageComment on Si̶ℓvεɾ Wølƒ's post “So how do you suppose the...”
(22 votes)
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Jessica
Posted 7 years ago. Direct link to Jessica's post “I don't understand how to...”
I don't understand how to rotate about the origin, please explain.
Button navigates to signup pageComment on Jessica's post “I don't understand how to...”
(3 votes)
Answer
- Jeremy Quilter
  Posted 7 years ago. Direct link to Jeremy Quilter's post “@garrettcummings22, I rea...”
  @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.
  Comment on Jeremy Quilter's post “@garrettcummings22, I rea...”
  (15 votes)
smile
Posted 9 months ago. Direct link to smile's post “i don't get this someone ...”
i don't get this someone help
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(9 votes)
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AlextheAnimator🎥
Posted 9 months ago. Direct link to AlextheAnimator🎥's post “How in the world do you r...”
How in the world do you rotate a point only using a simple coordinate plane? I did not think this would be so confusing.
Button navigates to signup pageComment on AlextheAnimator🎥's post “How in the world do you r...”
(9 votes)
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louisaandgreta
Posted 3 years ago. Direct link to louisaandgreta's post “I don’t see how it’s poss...”
I don’t see how it’s possible to rotate any polygon free-hand,without the rotation tool.
Button navigates to signup pageButton navigates to signup page
(7 votes)
Answer
- Fahmi Uddin Shah
  Posted a year ago. Direct link to Fahmi Uddin Shah's post “You could rotate each poi...”
  You could rotate each point of the polygon on its own, and then connect each point correctly. Remember that each point will be the same distance from the centre of rotation.
  Button navigates to signup page
  (4 votes)
_DEMARION_🦄👻😺👹
Posted 6 years ago. Direct link to _DEMARION_🦄👻😺👹's post “I think this lesson is be...”
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 :)
Button navigates to signup pageComment on _DEMARION_🦄👻😺👹's post “I think this lesson is be...”
(8 votes)
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- rojji
  Posted 4 years ago. Direct link to rojji's post “Yall get taught this in e...”
  Yall get taught this in eigth grade? while us asians go to school for 10hrs a day and we learn this in tenth grade
  Comment on rojji's post “Yall get taught this in e...”
  (1 vote)
lil jj
Posted a year ago. Direct link to lil jj's post “this is to hard make them...”
this is to hard make them easy again
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(8 votes)
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Kayla Brown
Posted 6 years ago. Direct link to Kayla Brown's post “I have to find the coordi...”
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.
Button navigates to signup pageButton navigates to signup page
(6 votes)
Answer
- p.m.
  Posted 6 years ago. Direct link to p.m.'s post “Great question! There ar...”
  Great question! There are actually several helpful shortcuts for finding rotations. For rotating 90 degrees counterclockwise about the origin, a point (x, y) becomes (-y, x). So for example, your N would become (4, -6).
  For more information, try this link: https://uploads.desmos.com/activitybuilder/3deb2fa7414964f508e36f7de7bfd615
  Comment on p.m.'s post “Great question! There ar...”
  (4 votes)
DarayS
Posted a year ago. Direct link to DarayS's post “what's the best way to le...”
what's the best way to learn algebra?.
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(7 votes)
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