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 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.

what way counter-clockwise go and what way does clockwise go.

Think about it this way: The direction at which a clock's second hand moves is clockwise. The opposite is counterclockwise

Main content

Basic geometry and measurement

Course: Basic geometry and measurement > Unit 14

Lesson 3: Rotations

Rotations review

CCSS.Math:

8.G.A.3

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 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.

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Alisa Zhupanenko
Posted 6 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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(38 votes)
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- ngoc
  Posted 5 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*)
  Button navigates to signup page
  (16 votes)
Si̶ℓvεɾ Wølƒ
Posted 7 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 ....
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Jessica
Posted 6 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.
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(1 vote)
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- Jeremy Quilter
  Posted 6 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...”
  (14 votes)
Kayla Brown
Posted 5 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
(8 votes)
Answer
- p.m.
  Posted 5 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...”
  (5 votes)
ED
Posted 9 months ago. Direct link to ED's post “The Fitness Gram™ Pacer T...”
The Fitness Gram™ Pacer Test
The FitnessGram™ Pacer Test is a multistage aerobic capacity test that progressively gets more difficult as it continues. The 20 meter pacer test will begin in 30 seconds. Line up at the start. The running speed starts slowly, but gets faster each minute after you hear this signal. [beep] A single lap should be completed each time you hear this sound. [ding] Remember to run in a straight line, and run as long as possible. The second time you fail to complete a lap before the sound, your test is over. The test will begin on the word start. On your mark, get ready, start.
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A🃏
Posted 23 days ago. Direct link to A🃏's post “⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉...”
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Button navigates to signup pageComment on A🃏's post “⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉...”
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- Ian Pulizzotto
  Posted 22 days ago. Direct link to Ian Pulizzotto's post “This is an unnecessary po...”
  This is an unnecessary post that only takes up space. It’s all gibberish.
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_DEMARION_🦄👻😺👹
Posted 5 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 :)
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- rojji
  Posted 3 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
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gamilah.alrabuoi@uascjstudent.org
Posted 3 years ago. Direct link to gamilah.alrabuoi@uascjstudent.org's post “what way counter-clockwis...”
what way counter-clockwise go and what way does clockwise go.
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- Victor
  Posted 3 years ago. Direct link to Victor's post “Think about it this way: ...”
  Think about it this way: The direction at which a clock's second hand moves is clockwise. The opposite is counterclockwise
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Dylan Fuel
Posted a month ago. Direct link to Dylan Fuel's post “Math?”
Math?
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ShinningStar
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⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀
⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿
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