In problem three I placed the rotation tool on P and rotated it 225 degrees but it is saying it is wrong!

I also made exactly this mistake. It says 255, not 225

What would be the default direction for rotation if it does not specify (counter clockwise or clockwise)??

when it puts - before the degrees it means counter clockwise and when there is no - it means clockwise

I didn't really understand how to do the challenge 1 problem. Perhaps give a tip on how to enter it using the computer.

STEP 1: Imagine that "orange" dot (that tool that you were playing with) is on top of point P. STEP 2: Point Q will be the point that will move clockwise or counter clockwise. STEP 3: When you move point Q to point R, you have moved it by 90 degrees counter clockwise (can you visualize angle QPR as a 90 degree angle?). STEP 4: When you move point Q to point S, you have moved it by 180 degrees counter clockwise (can you visualize QPS points when joined together as a straight line? Hence, 180 degree?). STEP 5: Remember that clockwise rotations are negative. So, when you move point Q to point T, you have moved it by 90 degrees clockwise (can you visualize angle QPT as a 90 degree angle?). Hence, you have moved point Q to point T by "negative" 90 degree. Hope that this helped.

In the options for answers what are those symbols?

those are lower case Greek letters which are often used to indicate measurement of angles. See https://www.ibiblio.org/koine/greek/lessons/alphabet.html. In the answers, you have the "ABCs" of the Greek alphabet, alpha, beta, gamma. You will also see these symbols used in Science at some point.

what happens if you rotate a dorito, is it still the same cos it's a triangle shape

As long as you do not take a bite out of it, yes you can rotate a dorito.

I can't really figure out what's being said in the explanation for the final question right. May someone please put it into layman's terms for me? Either that or just explain it to me like I'm a toddler. Thank you in advance.

So the image of C is C′. you connect these points to point P to find the angle formed by these lines which is α+β. i hope this is clear enough for you👍🏽

I do not under stand Challenge problem #2 WHAT IS THE EXPRESSION! Please give a answer that I can understand- I'm only in Gr5

These are letters of the Greek alphabet, known as alpha, beta, and I do not know the third. Like the letters in the standard alphabet used in math, these are also variables, and you will see them in later years.

I overall don't get the expression part. Like, I don't understand where it comes from or where to gather the info. I did try to use some common sense, but I want to be able how to do it without doubting myself and guessing.

Hi Debora, Few things you need to keep in mind when doing a rotation are- 1. The point of rotation (in most of the above examples, it is marked as P). 2. The angle of rotation. 3. Positive rotations are anti-clockwise and negative rotations are clockwise. When you start practicing rotations in the above examples, have a look at the line below the "Rotation Tab". This will tell you if you are on the right track or not. A game that you can play with your friends is by taking a rope, one of you can hold one end of it and the other one can hold the other end. Bring that cord on the floor/playground. One of you can be the center of rotation (point P) and the other person can move the other end of the cord clockwise or anti-clockwise around that center of rotation. You can move 90 degree (anti-clockwise) or minus 180 (clockwise)- these just two examples! Try to visualize it in your head and have fun with it- you can see how the shape is the same but its orientation has changed :-) Please feel free to ask any specific questions, if you have any. Happy learning. Aiena.

Main content

Basic geometry and measurement

Course: Basic geometry and measurement > Unit 14

Lesson 3: Rotations

Rotations intro

CCSS.Math:

Learn what rotations are and how to perform them in our interactive widget.

What is a rotation?

In the figure below, one copy of the trapezoid is rotating around the point.

In geometry, rotations make things turn in a cycle around a definite center point. Notice that the distance of each rotated point from the center remains the same. Only the relative position changes.

In the figure below, one copy of the octagon is rotated 22, degree around the point.

Notice how the octagon's sides change direction, but the general shape remains the same. Rotations don't distort shapes, they just whirl them around. Furthermore, note that the vertex that is the center of the rotation does not move at all.

Now that we've got a basic understanding of what rotations are, let's learn how to use them in a more exact manner.

The angle of rotation

Every rotation is defined by two important parameters: the center of the rotation—we already went over that—and the angle of the rotation. The angle determines by how much we rotate the plane about the center.

For example, we can tell that start color #ca337c, A, prime, end color #ca337c is the result of rotating start color #11accd, A, end color #11accd about P, but that's not exact enough.

In order to define the measure of the rotation, we look at the angle that's created between the segments start overline, P, A, end overline and start overline, P, A, prime, end overline.

This way, we can say that start color #ca337c, A, prime, end color #ca337c is the result of rotating start color #11accd, A, end color #11accd by 45, degree about P.

Clockwise and counterclockwise rotations

This is how we number the quadrants of the coordinate plane.

The quadrant numbers increase as we move counterclockwise. We measure angles the same way to be consistent.

Conventionally, positive angle measures describe counterclockwise rotations. If we want to describe a clockwise rotation, we use negative angle measures.

For example, here's the result of rotating a point about P by minus, 30, degree.

Pre-images and images

For any transformation, we have the pre-image figure, which is the figure we are performing the transformation upon, and the image figure, which is the result of the transformation. For example, in our rotation, the pre-image point was start color #11accd, A, end color #11accd, and the image point was start color #ca337c, A, prime, end color #ca337c.

Note that we indicated the image by start color #ca337c, A, prime, end color #ca337c—pronounced, "A prime". It is common, when working with transformations, to use the same letter for the image and the pre-image; simply add the prime suffix to the image.

Let's try some practice problems

Problem 1

Current

Plot the image of point A after a minus, 120, degree rotation about P.

Challenge problems

Challenge problem 1

Current

start color #ca337c, R, end color #ca337c, start color #ca337c, S, end color #ca337c, and start color #ca337c, T, end color #ca337c are all images of start color #11accd, Q, end color #11accd under different rotations.

Match each image with its appropriate rotation.

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eleanorms22
Posted 7 years ago. Direct link to eleanorms22's post “In problem three I placed...”
In problem three I placed the rotation tool on P and rotated it 225 degrees but it is saying it is wrong!
Button navigates to signup pageComment on eleanorms22's post “In problem three I placed...”
(45 votes)
Answer
- Petr Flosman
  Posted 5 years ago. Direct link to Petr Flosman's post “I also made exactly this ...”
  I also made exactly this mistake. It says 255, not 225
  Comment on Petr Flosman's post “I also made exactly this ...”
  (18 votes)
carrie_riffee
Posted 7 years ago. Direct link to carrie_riffee's post “I didn't really understan...”
I didn't really understand how to do the challenge 1 problem. Perhaps give a tip on how to enter it using the computer.
Button navigates to signup pageComment on carrie_riffee's post “I didn't really understan...”
(12 votes)
Answer
- Aiena
  Posted 7 years ago. Direct link to Aiena's post “STEP 1: Imagine that "ora...”
  STEP 1: Imagine that "orange" dot (that tool that you were playing with) is on top of point P.
  STEP 2: Point Q will be the point that will move clockwise or counter clockwise.
  STEP 3: When you move point Q to point R, you have moved it by 90 degrees counter clockwise (can you visualize angle QPR as a 90 degree angle?).
  STEP 4: When you move point Q to point S, you have moved it by 180 degrees counter clockwise (can you visualize QPS points when joined together as a straight line? Hence, 180 degree?).
  STEP 5: Remember that clockwise rotations are negative. So, when you move point Q to point T, you have moved it by 90 degrees clockwise (can you visualize angle QPT as a 90 degree angle?). Hence, you have moved point Q to point T by "negative" 90 degree.
  
  Hope that this helped.
  Comment on Aiena's post “STEP 1: Imagine that "ora...”
  (38 votes)
Laya Ghosn
Posted 5 years ago. Direct link to Laya Ghosn's post “What would be the default...”
What would be the default direction for rotation if it does not specify (counter clockwise or clockwise)??
Button navigates to signup pageComment on Laya Ghosn's post “What would be the default...”
(25 votes)
Answer
- Naomi
  Posted 3 years ago. Direct link to Naomi's post “when it puts - before the...”
  when it puts - before the degrees it means counter clockwise and when there is no - it means clockwise
  Comment on Naomi's post “when it puts - before the...”
  (5 votes)
Meimei
Posted 5 years ago. Direct link to Meimei's post “In the options for answer...”
In the options for answers what are those symbols?
Button navigates to signup pageButton navigates to signup page
(11 votes)
Answer
- David Severin
  Posted 5 years ago. Direct link to David Severin's post “those are lower case Gree...”
  those are lower case Greek letters which are often used to indicate measurement of angles. See https://www.ibiblio.org/koine/greek/lessons/alphabet.html. In the answers, you have the "ABCs" of the Greek alphabet, alpha, beta, gamma. You will also see these symbols used in Science at some point.
  Comment on David Severin's post “those are lower case Gree...”
  (10 votes)
Bryce
Posted 2 years ago. Direct link to Bryce's post “what happens if you rotat...”
what happens if you rotate a dorito, is it still the same cos it's a triangle shape
Button navigates to signup pageComment on Bryce's post “what happens if you rotat...”
(10 votes)
Answer
- David Severin
  Posted 2 years ago. Direct link to David Severin's post “As long as you do not tak...”
  As long as you do not take a bite out of it, yes you can rotate a dorito.
  Comment on David Severin's post “As long as you do not tak...”
  (11 votes)
Oakley Gatewood
Posted 4 years ago. Direct link to Oakley Gatewood's post “I can't really figure out...”
I can't really figure out what's being said in the explanation for the final question right. May someone please put it into layman's terms for me? Either that or just explain it to me like I'm a toddler. Thank you in advance.
Button navigates to signup pageButton navigates to signup page
(10 votes)
Answer
- Helen Ω
  Posted 4 years ago. Direct link to Helen Ω's post “So the image of C is C′. ...”
  So the image of C is C′. you connect these points to point P to find the angle formed by these lines which is α+β. i hope this is clear enough for you👍🏽
  Comment on Helen Ω's post “So the image of C is C′. ...”
  (7 votes)
thaisb2
Posted 25 days ago. Direct link to thaisb2's post “Im so confused as an 8th ...”
Im so confused as an 8th grader doing this. 😭
Button navigates to signup pageComment on thaisb2's post “Im so confused as an 8th ...”
(15 votes)
Answer
- jay
  Posted 6 days ago. Direct link to jay's post “which part”
  which part
  Button navigates to signup page
  (1 vote)
Linsday Langley
Posted 3 years ago. Direct link to Linsday Langley's post “I need more help understa...”
I need more help understanding rotations a little bit more.
Button navigates to signup pageComment on Linsday Langley's post “I need more help understa...”
(11 votes)
Answer
Debora Canales
Posted 7 years ago. Direct link to Debora Canales's post “I overall don't get the e...”
I overall don't get the expression part. Like, I don't understand where it comes from or where to gather the info. I did try to use some common sense, but I want to be able how to do it without doubting myself and guessing.
Button navigates to signup pageButton navigates to signup page
(7 votes)
Answer
- Aiena
  Posted 7 years ago. Direct link to Aiena's post “Hi Debora, Few things yo...”
  Hi Debora,
  
  Few things you need to keep in mind when doing a rotation are-
  1. The point of rotation (in most of the above examples, it is marked as P).
  2. The angle of rotation.
  3. Positive rotations are anti-clockwise and negative rotations are clockwise.
  
  When you start practicing rotations in the above examples, have a look at the line below the "Rotation Tab". This will tell you if you are on the right track or not.
  
  A game that you can play with your friends is by taking a rope, one of you can hold one end of it and the other one can hold the other end. Bring that cord on the floor/playground. One of you can be the center of rotation (point P) and the other person can move the other end of the cord clockwise or anti-clockwise around that center of rotation. You can move 90 degree (anti-clockwise) or minus 180 (clockwise)- these just two examples!
  
  Try to visualize it in your head and have fun with it- you can see how the shape is the same but its orientation has changed :-)
  
  Please feel free to ask any specific questions, if you have any.
  
  Happy learning.
  
  Aiena.
  Comment on Aiena's post “Hi Debora, Few things yo...”
  (8 votes)
Gurnoor
Posted 3 years ago. Direct link to Gurnoor's post “I do not under stand Chal...”
I do not under stand Challenge problem #2
WHAT IS THE EXPRESSION!
Please give a answer that I can understand- I'm only in Gr5
Button navigates to signup pageButton navigates to signup page
(8 votes)
Answer
- nr0193954
  Posted 3 years ago. Direct link to nr0193954's post “These are letters of the ...”
  These are letters of the Greek alphabet, known as alpha, beta, and I do not know the third. Like the letters in the standard alphabet used in math, these are also variables, and you will see them in later years.
  Button navigates to signup page
  (5 votes)