Rotating Points Around the Origin
To solve the question in the image, we need to determine the new positions of the vertices after a 270° counterclockwise rotation around the origin.
The original coordinates of the vertices appear to be:
- J(6,3)
- K(9,3)
- L(6,-2)
Here are the general rules for rotating points around the origin:
- For a 90° counterclockwise rotation, (x, y) becomes (-y, x).
- For a 180° rotation, (x, y) becomes (-x, -y).
- For a 270° counterclockwise rotation, (x, y) becomes (y, -x).
Applying the rule for a 270° rotation to each point:
For J(6,3):
Rotate 270° counterclockwise to get J'(3,-6).
For K(9,3):
Rotate 270° counterclockwise to get K'(3,-9).
For L(6,-2):
Rotate 270° counterclockwise to get L'(-2,-6).
Therefore, the new coordinates after the 270° counterclockwise rotation around the origin are:
- J'(3, -6)
- K'(3, -9)
- L'(-2, -6)
