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### Course: Geometry (all content)>Unit 10

Lesson 9: Old transformations videos

# Rotation examples (old)

An older video where Sal finds the images of shapes under various rotations, and where he determines the rotations that take one shape to another. Created by Sal Khan.

## Want to join the conversation?

• It would be helpful if you incorporated the algebraic steps to these results, i.e. how the x and y change for 90, 180 and 270 rotations. Problems often require this approach, and it's more useful, especially when the shape does not have a point on either axis (or there is no shape at all, i.e. just points given).
• When you rotate exactly 90 degrees around the origin, you will cross one axis. So take the (x,y) coordinates for the point, and see which axis would be crossed. In the rotated point, the x-value and y-value swap places. Then, whichever one doesn't match the axis that got crossed becomes negative.

Here's an example: "Rotate the point (4,1) around the origin by 90 degrees". The coordinates for the rotated point will be (-1,4). The 4 and the 1 swapped places, then the x-value became negative because the y-axis got crossed.

To rotate 180 or 270 degrees, you could keep rotating the point by 90 degrees until you arrive where you need to be. Or you could just memorize that rotating 180 degrees around the origin means both the x-value and the y-value become negative, without swapping places. So (2,3) rotated 180 degrees around the origin would be (-2,-3). Rotating 270 degrees is the same as rotating 90 degrees in the opposite direction.
• How do you find the rotation if it's not at the origin?
• Find the translation needed to move the center of rotation to the origin, apply that to the shape, perform your rotation, and then undo the original transformation
• what are the rules for rotation like if you go 90 degrees clockwise would you switch the coordinates and make one negative? I would like to know the rules for if you go 90 degrees counterclockwise, 90 degrees clockwise, 180 degrees counterclockwise, 180 degrees clockwise, 270 degrees counterclockwise, and finally 270 degrees clockwise. please help !!
• 90 clockwise and 270 counter clockwise are the same thing
90 counter clockwise and 270 clockwise are the same thing
180 clockwise and 180 counter clockwise are the same thing

90 counter clockwise would be (-y, x)
90 clockwise would be (y,-x)
180 either way would be (-x,-y)
• Is rotating by -90 the same as rotating by 270?

(all measures are in degrees)
• You will end up facing the same direction, but one of them might leave you a bit dizzier.
• i still do not get how to solve this...are there any easy tricks for solving this?
• Take it slow and cut a shape like it and try rotating it that way
• Why is the positive direction counterclockwise? This seems counterintuitive.
• Just look at a protractor and you will understand. The 0 degrees is on the right side and the numbers go counterclockwise.
• for a rotational translation, does that mean the shape is rotated AND translated?
• at , it said you should go into counterclockwise direction. Why cant we go in clockwise direction?
Also, when you are dealing with shapes irregularly put in position, how would you know if it is 90 degrees?