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

Lesson 3: Rotations

# Rotating points

Positive rotation angles mean we turn counterclockwise. Negative angles are clockwise. We can think of a 60 degree turn as 1/3 of a 180 degree turn. A 90 degree turn is 1/4 of the way around a full circle. The angle goes from the center to first point, then from the center to the image of the point.

## Want to join the conversation?

• So just to confirm what Sal briefly explained in the video, a positive number of degrees means you rotate counterclockwise, while a negative number of degrees means you rotate clockwise, correct?
• Seems a bit un-intuitive but since the 1st quadrant starts from right and goes to left, adding positive number of degree means you go towards left i.e. you rotate counter-clockwise and vice versa.
• Are there formulas to do 90,180,270, rotations around a point that is not the origin?
• Four years late, but here it is.
Yes, there are. I was learning about this to help with a diagnostic. All you have to do is make the point you´re rotating around the new origin. You might have to tilt the whole coordinate plane, or even chop off parts of it and make new areas.
• Is rotating basically just eyeballing the correct angle?
• For these exercises, it is my impression that you are best served by eyeballing.

If you want to get more precise, you would use an instrument that measures angles (the most common example is a protractor) and verify that your point-to-point mappings satisfy the rotation angle requirement. You would also want to make sure that distances from the point of rotation are the same. Most protractors also have a limited ruler along the edge.
• Why do you have to rotate counterclockwise if the angle is
positive, and clockwise if the angle is negative?
• It goes back to the unit circle where 0 degrees is along the positive x axis. All our angles greater than 0 and less than 90 (positive y axis) are in the first quadrant (positive x, positive y), so this is that counterclockwise rotation.
• Why is that when he was talking about going to the positive direction, he went left, and when he was talking about the negative direction he when right. Shouldn't it be the opposite way around?
• A positive rotation is in the counterclockwise direction. With unit circle theory, the positive x axis is 0 degrees, so rotating into the first quadrant gives positive values for sin and cos which make best sense for angles between 0 and 90.
• How do we know whether to go counter-clockwise or clockwise as it didn't say so in this question...

EDIT: Saw the video again and am now confused on why positive degrees means counter-clockwise and negative degrees mean clockwise! I mean it feels more satisfactory for the positive degrees to be clockwise and the negative degrees to be counter-clockwise!
• Vote this question if your wondering what app this guy is using.
• He literally just uses the old version of khan academy.
(They made the videos before this version.)
(1 vote)
• Sal: Makes an explainer video to explain rotation
Sal: Doesn't explain rotation.

Positive rotation is going in the negative/counter-clockwise direction. You forgot to actually explain that, haha.