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
Rotation Symmetry 5083Da
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