Subjects geometry

Rotation 180 Cfc51A

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1. The problem asks to describe the single transformation mapping shape A to shape B for part (a). 2. From the description, triangle A at approximately $(-2,3)$ is rotated 180° around the origin to map onto triangle B at approximately $(2,-3)$. 3. The formula for a rotation of 180° about the origin is: $$ (x,y) \to (-x,-y) $$ This means each point $(x,y)$ of the original shape is mapped to $(-x,-y)$ after rotation. 4. Applying this to point $(-2,3)$: $$ (-2,3) \to (-(-2), -(3)) = (2,-3) $$ which matches the location of triangle B. 5. Therefore, the single transformation is a rotation of 180° about the origin. 6. This rotation flips the shape across the origin, turning every point to its opposite in both x and y coordinates. Final answer: The transformation is a rotation of 180° about the origin.