How Do You Rotate a Figure 90 Degrees Around the Origin?

'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

1. The original figure is located in Quadrant II
2. Coordinate pairs are also called ordered pairs
1. An x-value is simply an x-coordinate, and a y-value is a y-coordinate
2. Our original coordinates are: (-4,1), (-4,4), (-2,1), (-1,4)
3. Notice that only the x-coordinate gets its sign flipped for this rotation
4. So positives become negative and negatives become positive
5. Our figure started with all negative x-coordinates, so they all become positive
6. This will move our figure into Quadrant I, where the x- and y-coordinates are always positive
1. This is the last step for rotating our figure!
2. In Step 2, we updated our ordered pairs to be:
3. (4,1), (4,4), (2,1), (1,4)
4. We now have the coordinates for our rotated image!
5. The image is the figure that is created after we transform the original figure
1. There is a formula for rotating objects 90 degrees around the origin!
2. (x,y) --> (y,-x)
3. An x-value is simply an x-coordinate, and a y-value is a y-coordinate
4. 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!
5. That means you'd be switching the sign of the NEW y-coordinates after you switch x and y

Rotate a figure 90 degrees about the origin.