Question

What are the coordinate points of
A
′
A
′

(
8
,

5
)
(8, 5) if
A
A undergoes a rotation of:



90
°
90° clockwise



180
°
180° clockwise




270
°
270° clockwise

Answer 1

To find the coordinate points of \( A' \) after various rotations of point \( A(8, 5) \), we can use the following rules for rotation:

1. **90° clockwise rotation**: The new coordinates will be \( (y, -x) \).
2. **180° clockwise rotation**: The new coordinates will be \( (-x, -y) \).
3. **270° clockwise rotation**: The new coordinates will be \( (-y, x) \).

Now, let's apply these rules to the point \( A(8, 5) \):

### 1. 90° Clockwise Rotation
Using the rule:
\[
(x, y) \to (y, -x)
\]
For \( A(8, 5) \):
\[
A' = (5, -8)
\]

### 2. 180° Clockwise Rotation
Using the rule:
\[
(x, y) \to (-x, -y)
\]
For \( A(8, 5) \):
\[
A' = (-8, -5)
\]

### 3. 270° Clockwise Rotation
Using the rule:
\[
(x, y) \to (-y, x)
\]
For \( A(8, 5) \):
\[
A' = (-5, 8)
\]

### Summary of Coordinates after Rotations:
- **90° clockwise**: \( (5, -8) \)
- **180° clockwise**: \( (-8, -5) \)
- **270° clockwise**: \( (-5, 8) \)