When a figure (like EFG) is rotated -90 degrees clockwise to create a new figure (like XYZ), several properties and relationships remain consistent. Here are some statements that must be true after such a rotation:
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Position Change: The points will change their coordinates based on the rotation. If the original coordinates of points E, F, and G are known, their new coordinates in XYZ can be determined using the rotation matrix for -90 degrees clockwise.
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Shape Preservation: The shape of the figure EFG will remain the same after rotation; it will still be the same type of figure (triangles remain triangles, etc.).
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Angle Preservation: The angles between corresponding sides will remain unchanged. The internal angles of EFG will still equal the internal angles of XYZ.
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Orientation Change: The orientation of the figure will change. For example, if EFG is oriented in a certain way, XYZ will be oriented differently.
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Distance Preservation: The distance between any two points (for instance between E and F, or F and G) will be preserved after rotation.
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Area Preservation: The area of the figure will remain the same before and after rotation.
Therefore, the exact statements that must be true depend on the specific context, such as the type of figure you are working with (triangle, polygon, etc.). However, the core principle of rotation maintaining size, shape, angle measures, and distances while changing position and orientation is always true.