Question

question
what is the image point of (1, -3) after the transformation ( r_{90^circ} circ r_{y\text{-axis}} )?
answer attempt 1 out of 2
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Explanation:

Step1: Apply \( r_{y\text{-axis}} \)

The reflection over the \( y \)-axis, \( r_{y\text{-axis}} \), transforms a point \( (x, y) \) to \( (-x, y) \). For the point \( (1, -3) \), applying \( r_{y\text{-axis}} \) gives \( (-1, -3) \).

Step2: Apply \( R_{90^\circ} \)

The rotation \( R_{90^\circ} \) (counterclockwise) transforms a point \( (x, y) \) to \( (-y, x) \). Now take the result from Step 1, \( (-1, -3) \), and apply \( R_{90^\circ} \). Substituting \( x = -1 \) and \( y = -3 \) into the rotation formula, we get \( -(-3) = 3 \) (new \( x \)-coordinate) and \( -1 \) (new \( y \)-coordinate). So the point becomes \( (3, -1) \).

Answer:

\( (3, -1) \)