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How Do You Rotate a Figure 90 Degrees Around the Origin?
Rotate a figure 90 degrees about the origin.
Summary
- 'x' and 'y' label the x and y-axes
- The origin is the point (0,0)
- The center of rotation, the origin, is the point we're rotating our figure around
- The figure in Quadrant I is the rotated image, the figure in Quadrant II is the original figure
- The 'image' is the figure that is created after we transform it
- To rotate a figure 90 degrees around the origin, switch the signs of the x-values, then switch the x- and y-coordinates

Notes
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- The original figure is located in Quadrant II
- Coordinate pairs are also called ordered pairs
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- An x-value is simply an x-coordinate, and a y-value is a y-coordinate
- Our original coordinates are: (-4,1), (-4,4), (-2,1), (-1,4)
- Notice that only the x-coordinate gets its sign flipped for this rotation
- So positives become negative and negatives become positive
- Our figure started with all negative x-coordinates, so they all become positive
- This will move our figure into Quadrant I, where the x- and y-coordinates are always positive
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- This is the last step for rotating our figure!
- In Step 2, we updated our ordered pairs to be:
- (4,1), (4,4), (2,1), (1,4)
- We now have the coordinates for our rotated image!
- The image is the figure that is created after we transform the original figure
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- There is a formula for rotating objects 90 degrees around the origin!
- (x,y) --> (y,-x)
- An x-value is simply an x-coordinate, and a y-value is a y-coordinate
- If you switch the x- and y-coordinates first, be careful that you switch the signs on the original x-coordinates in the second step!
- That means you'd be switching the sign of the NEW y-coordinates after you switch x and y