When a geometric figure, such as a triangle or a polygon, is rotated -90 degrees (clockwise), several characteristics about the figure will change based on rotation. Here are some general statements that can be considered true after such a rotation:
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Orientation Changes: The orientation of points (vertices) in EFG will change; in particular, if you label the vertices of EFG as E, F, and G, after a -90 degree rotation, they will be rearranged in the new positions X, Y, and Z.
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Coordinates Transformation: If we consider the mathematical representation of points in a Cartesian coordinate system, each point (x, y) transforms during a -90 degree clockwise rotation to (y, -x). Therefore, the coordinates of each point in triangle EFG will change to reflect this transformation.
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Area Preservation: The area enclosed by EFG and XYZ will remain the same. Rotation is a rigid transformation that does not alter the shape or size of the figure.
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Distance Preservation: The distances between any two points in EFG will be preserved in XYZ. Thus, if you measure the distance between points E and F in EFG, it will be identical to the distance between points X and Y in XYZ.
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Angle Measures: The angles between any two sides in EFG will be the same after rotation in XYZ; the angles are preserved in rigid transformations.
While the exact statements that must be true depend on the detailed context of EFG's configuration, these general properties of geometric transformations will always apply. If there are specific options you are considering, feel free to share, and I can help evaluate their truth!