Question

A rotation maps point A(5, 4) to A’(–4, 5).


Which describes the rotation?
180° clockwise rotation
180° counterclockwise rotation
90° counterclockwise rotation
90° clockwise rotation

Answer 1

To determine the rotation that maps point \( A(5, 4) \) to \( A'(-4, 5) \), we can analyze the coordinates.

1. **90° Counterclockwise Rotation**: The rule for a 90° counterclockwise rotation is:
\[
(x, y) \to (-y, x)
\]
Applying this to \( A(5, 4) \):
\[
(5, 4) \to (-4, 5)
\]
This matches \( A'(-4, 5) \).

2. **90° Clockwise Rotation**: The rule for a 90° clockwise rotation is:
\[
(x, y) \to (y, -x)
\]
Applying this to \( A(5, 4) \):
\[
(5, 4) \to (4, -5)
\]
This does not match \( A'(-4, 5) \).

3. **180° Counterclockwise Rotation**: The rule for a 180° rotation (either direction) is:
\[
(x, y) \to (-x, -y)
\]
Applying this to \( A(5, 4) \):
\[
(5, 4) \to (-5, -4)
\]
This does not match \( A'(-4, 5) \).

4. **180° Clockwise Rotation**: The rule for a 180° rotation is the same as counterclockwise:
\[
(5, 4) \to (-5, -4)
\]
This also does not match \( A'(-4, 5) \).

Since only the 90° counterclockwise rotation produces the correct transformation from \( A(5, 4) \) to \( A'(-4, 5) \), the rotation that describes the transformation is:

**90° counterclockwise rotation.**