Question

multiple answer 1 point which transformations are rigid motions? dilation with a k = 1 reflection over any line. translation in any direction. dilation with k ≠ 1 rotation around any point, direction, and degree.

Explanation:

• Reflection over any line: A reflection is a rigid motion as it preserves the shape and size of the figure. The distance between any two points in the original figure and their images after reflection remains the same.
• Translation in any direction: A translation is a rigid motion. When a figure is translated, every point of the figure is moved the same distance in the same direction. The shape and size of the figure do not change.
• Rotation around any point, direction, and degree: A rotation is a rigid motion. It preserves the distances between points (the shape and size of the figure). The angle measures and side lengths of the figure remain unchanged.
• Dilation with \(k = 1\): A dilation with \(k=1\) is equivalent to the identity transformation (the figure maps onto itself). Since it does not change the size (as \(k = 1\)) and shape (as it is a dilation with a non - zero scale factor), it is a rigid motion.
• **Dilation with \(k

eq1\)**: A dilation with \(k
eq1\) changes the size of the figure. If \(|k|> 1\), the figure is enlarged and if \(0<|k|<1\), the figure is reduced. Since the size of the figure changes, it is not a rigid motion.

Answer:

A. Dilation with a \(k = 1\)
B. Reflection over any line
C. Translation in any direction
E. Rotation around any point, direction, and degree