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## Grade 8 math (FL B.E.S.T.)

### Course: Grade 8 math (FL B.E.S.T.)>Unit 8

Lesson 3: Rotations

# Determining rotations

To see the angle of rotation, we draw lines from the center to the same point in the shape before and after the rotation. Counterclockwise rotations have positive angles, while clockwise rotations have negative angles. Then we estimate the angle. For example, 30 degrees is 1/3 of a right angle.

## Want to join the conversation?

• is there any way to find out how many degrees to turn it without guess and check?
• Well, I guess you can do it by looking at the coordinates and calculating it, but it's too complicated to explain and not worth doing. Since they give you an actual model of it when rotating, just give it a rough estimate and plug it in. That's all I can say. :)
• why is he saying prime? when he says a letter
• In the video:
ΔA'B'C' is the image of ΔABC under a rotation about the origin, (0, 0).

The source, ΔABC, is read "triangle A B C"

The image, ΔA'B'C', is read "triangle A-prime B-prime C-prime"
- this is the triangle you get after the rotation

Using the suffix "prime" after each point lets us know that he is talking about the image of the rotation (not the source of the rotation).

Hope this helps!
• How do i tell if the rotation is negative is posative or negative?
• By convention, counter-clockwise rotation is positive, clockwise rotation is negative.
• But how do we know which way the shape was rotated? It could be any way. Sometimes the two shapes are really far apart and its really hard to tell.
• When you have practiced this enough, you should be able to tell the 4 general rotations (90 degrees, 180 degrees, and 270 degrees) counterclockwise (positive direction), and thus their equivalents (270 degrees, 180 degrees, and 90 degrees) clockwise. Whit this, you can at least be able to figure out a lot of limitations. so looking at the picture in the video, you should be able to see that it is < 90 counterclockwise (between 0 to 90) and which would be >270 clockwise (between - 270 and - 360 degrees). While it may not always give the answer, it generally eliminates 2 of 4 answers.
• Is there a reason it is called a prime?
• Yes, there is a reason it is called a prime!

Using the suffix "prime" after each point of ΔA'B'C' - "A-prime B-prime C-prime" - lets us know that we are talking about the image of the rotation, and not the source of the rotation (ΔABC, the triangle we started with).

Hope this helps!
• Could you make a video with some formulas?
• The formulas require sufficient knowledge of trigonometry & such. Rotation is used all the time in programming to make objects rotate, and is often combo-ed with linear algebra to make the cool effects you'll see in games & animations.

Khan Academy collaborated with Pixar to make this series of videos, where they teach you about deriving that formula: https://www.khanacademy.org/computing/pixar/sets/rotation/a/rotation-lesson-brief
• Why does the positive angle turn `Counterclockwise` and a protractor measured as `Clockwise`?

Why We Can't Just change the positive angle to "`clockwise`" that we will not mixed up together?

• It has to do with the unit circle and the trig functions. Since the 1st quadrant is positive x and positive y, it makes sense that the basic trig functions are within this quadrant. So the angles between 0 and 90 are in the first quadrant and require the counterclockwise rotation. Clockwise would put the angles in the positive x negative y fourth quadrant.
• How is it a positive angel?
• We define rotations in the counter-clockwise direction as positive and those going clockwise as negative. This is just an established convention, and if you wanted to do it the other way, you would have to restructure a fair amount of math.