Which shows the proper coordinate notation for a rotation that is 180 degrees clockwise about the origin
A. (3,6)->(6,3)
B. (3,6)->(-3,6)
c. (3,6)->(6,-3)
D. (3,6)->(-3,-6)
HELP please? Thanks
Hint:
rotation of 180 about the origin would be of the form:
(x,y)->(-x,-y)
To determine the proper coordinate notation for a rotation that is 180 degrees clockwise about the origin, you can follow these steps:
1. Start with the original coordinates of the point.
In this case, the original coordinates are (3,6).
2. Apply the rotation by performing the following calculations:
- The x-coordinate of the rotated point will be the negation of the original y-coordinate.
- The y-coordinate of the rotated point will be the negation of the original x-coordinate.
Let's apply these calculations to each option:
Option A: (3,6) -> (6,3)
- The x-coordinate of the rotated point is 6, which is not the negation of the original y-coordinate, so this option is incorrect.
Option B: (3,6) -> (-3,6)
- The x-coordinate of the rotated point is -3, which is not the negation of the original y-coordinate, so this option is incorrect.
Option C: (3,6) -> (6,-3)
- The x-coordinate of the rotated point is 6, which is not the negation of the original y-coordinate, so this option is incorrect.
Option D: (3,6) -> (-3,-6)
- The x-coordinate of the rotated point is -3, which is the negation of the original y-coordinate.
- The y-coordinate of the rotated point is -6, which is the negation of the original x-coordinate.
Therefore, the proper coordinate notation for a rotation that is 180 degrees clockwise about the origin is (3,6) -> (-3,-6), which corresponds to option D.