Subjects geometry

Rotation Symmetry 5083Da

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1. The problem asks to identify the transformation illustrated by the graph. 2. The graph shows two shapes: one in the top-left quadrant and one in the bottom-right quadrant. 3. The points in the top-left are (-3,4), (-2,2), (-1,3). 4. The points in the bottom-right are (2,-4), (3,-2), (4,-3). 5. Notice that each point in the bottom-right is the result of rotating the corresponding top-left point by 180° about the origin. 6. The formula for a 180° rotation about the origin is: $$ (x,y) \to (-x,-y) $$ 7. Applying this to (-3,4): $$ (-3,4) \to (3,-4) $$ 8. The point (3,-4) matches the bottom-right point (3,-4) after swapping order, so the shape is rotated 180°. 9. Therefore, the transformation is a 180° rotation about the origin. 10. For the second question, which letter has at least one line of symmetry? - F has no line of symmetry. - R has no line of symmetry. - O is perfectly symmetrical with infinite lines of symmetry. Final answers: 1) b) 180° rotation about the origin 2) c) O