Questions: Describe a congruence transformation that maps the blue preimage to the green image. a 270° rotation about the origin a reflection in the line y=-1 a reflection in the line y=-x a 180° rotation about the origin

Describe a congruence transformation that maps the blue preimage to the green image.
a 270° rotation about the origin a reflection in the line y=-1
a reflection in the line y=-x a 180° rotation about the origin

Transcript text: Describe a congruence transformation that maps the blue preimage to the green image. a $270^{\circ}$ rotation about the origin a reflection in the line $y=-1$ a reflection in the line $y=-x$ a $180^{\circ}$ rotation about the origin

Solution

Solution Steps

Step 1: Analyze the transformation

The blue preimage is transformed to the green image. Observe the orientation of the figures. The preimage WXYZ has W in the top left, X in the top right, Z bottom left, and Y bottom right. The image PQRS has P in the bottom right, Q bottom left, R top left, and S top right. This suggests a rotation.

Step 2: Determine the rotation angle

Consider point X at (-2, 4). After a 270° counterclockwise rotation about the origin, X would map to (4, 2). This aligns with the location of point R. Similarly, point W(-5, 4) after a 270° rotation becomes (4, 5), which corresponds to the position of S. Point Y(-1, 1) rotates to (1, 1) which is point Q, and Z(-5, 1) rotates to (1, 5) which is point P.

Final Answer: The transformation is a 270° rotation about the origin.

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