What is the rule for a $$ 270^{\circ} $$ counterclockwise rotation? Select one: a. $$ (x, y) \rightarrow(-y,-x) $$ b. $$ (x, y) \rightarrow(y,-x) $$ c. $$ (x, y) \rightarrow(y, x) $$ d. $$ (x, y) \rightarrow(-y, x) $$

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To find the rule for a $$ 270^{\circ} $$ counterclockwise rotation, we use the rotation transformation formulas. For any rotation by an angle $$ \theta $$, the new coordinates $$(x', y')$$ are given by:

$$
x' = x \cos \theta - y \sin \theta \quad \text{and} \quad y' = x \sin \theta + y \cos \theta.
$$

Here, $$ \theta = 270^{\circ} $$. We know that:

$$
\cos 270^{\circ} = 0 \quad \text{and} \quad \sin 270^{\circ} = -1.
$$

Substitute these values into the formulas:

$$
x' = x(0) - y(-1) = y,
$$
$$
y' = x(-1) + y(0) = -x.
$$

Thus, the transformation rule is:

$$
(x, y) \rightarrow (y, -x).
$$

The correct answer is option b.
The rule for a $$ 270^{\circ} $$ counterclockwise rotation is $$ (x, y) \rightarrow (y, -x) $$.

What is the rule for a \( 270^{\circ} \) counterclockwise rotation? Select one: a. \( (x, y) \rightarrow(-y,-x) \) b. \( (x, y) \rightarrow(y,-x) \) c. \( (x, y) \rightarrow(y, x) \) d. \( (x, y) \rightarrow(-y, x) \)

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