Under rotations, certain properties of objects remain unchanged. These include:
Shape: The overall shape of an object is preserved after a rotation. For example, a square remains a square and a circle remains a circle after a rotation.
Orientation: The relative positions of the sides or angles of an object are preserved. For instance, in a square, the sides will always be perpendicular to each other after a rotation.
Length: The lengths of the sides or the radii of an object are also preserved. If a triangle has side lengths of 4 cm, 5 cm, and 6 cm before a rotation, these lengths will remain the same after the rotation.
However, certain properties of objects do change under rotations. These include:
Position: The position of an object in the coordinate plane will generally change after a rotation. Points may be shifted horizontally, vertically, or both.
Angle measures: The measures of angles in an object will change after a rotation. For example, a 90-degree angle may become a 45-degree angle after a rotation.
Orientation: The direction in which an object is facing may change. For instance, if a shape is originally facing upwards, it may face a different direction after a rotation.
Understanding these properties is crucial when analyzing the effects of rotations on objects and their attributes. By recognizing what remains the same and what changes, students can accurately predict transformations and analyze their impact.