Question

What are the coordinate points of A′ if A (5, 6) undergoes a rotation of:(Click Here for Help Video 1. Click Here for Help Video 2.)(2 points)90°clockwise:270°clockwise:

Answer 1

To find the coordinates of point \( A' \) after a rotation of point \( A(5, 6) \), we can use the following rules for rotation about the origin:

1. **90° clockwise rotation**:
The transformation for a 90° clockwise rotation is given by:
\[
(x, y) \to (y, -x)
\]
Applying this to point \( A(5, 6) \):
\[
A'(5, 6) \to (6, -5)
\]
So, the new coordinates after a 90° clockwise rotation are \( A' = (6, -5) \).

2. **270° clockwise rotation**:
A 270° clockwise rotation is equivalent to a 90° counterclockwise rotation, and the transformation is:
\[
(x, y) \to (-y, x)
\]
Applying this to point \( A(5, 6) \):
\[
A'(5, 6) \to (-6, 5)
\]
Thus, the new coordinates after a 270° clockwise rotation are \( A' = (-6, 5) \).

In summary:
- After a **90° clockwise rotation**, the coordinates are \( A' = (6, -5) \).
- After a **270° clockwise rotation**, the coordinates are \( A' = (-6, 5) \).