To perform a 270-degree clockwise rotation about the origin, you can use the following transformation rule for coordinates (x, y):
For a 270-degree clockwise rotation:
- The new coordinates (x', y') are given by:
- \( x' = y \)
- \( y' = -x \)
Let's apply this transformation to Y's coordinates. Since you did not specify the original coordinates of Y, let's assume that Y is (x, y).
After applying the rotation:
- \( x' = y \)
- \( y' = -x \)
Now, let me verify the answer choices given:
- Y' (1, -9)
- Y' (1, 9)
- Y' (-1, 9)
- Y' (-9, 1)
To find the coordinates after a 270-degree clockwise rotation, you would substitute the actual coordinates of Y into the transformation formulas provided above.
To help narrow down the selection, if we compare the transformations with the answers, let's analyze:
For (1, 9):
- \( x' = 9 \)
- \( y' = -1 \) -> (9, -1)
For (1, -9):
- \( x' = -9 \)
- \( y' = -1 \) -> (-9, -1)
For (-1, 9):
- \( x' = 9 \)
- \( y' = 1 \) -> (9, 1)
For (-9, 1):
- \( x' = 1 \)
- \( y' = -9 \) -> (1, -9)
If you are asking for the transformation of Y directly to one of the answer points without knowing Y's original coordinates, please clarify that, or provide the original coordinates for accurate rotation calculation.
Based on the given selections, if original Y's coordinates were (9, 1), for example, the transformed point after a 270-degree clockwise rotation would equal Y' (-1, 9), which aligns correctly with option three.
If you can provide the original coordinates or further specify the problem context, I could assist further.