Is the statement always true, sometimes true or never true. and why.

Question

Is the statement always true, sometimes true or never true. and why. A polygon with clockwise orientation will still have clockwise orientation after performing a rigid motion.

Answer 1

A rigid motion is a transformation that preserves the shape and size of a figure, such as a translation, rotation, or reflection.

1. Translation or Rotation:
2. These transformations do not change the orientation of a polygon.
3. If a polygon has clockwise orientation before a translation or rotation, it will still have a clockwise orientation afterward.
4. Result: Orientation is preserved.
5. Reflection:
6. A reflection flips the polygon across a line, which reverses its orientation.
7. If the polygon has clockwise orientation before a reflection, it will have a counterclockwise orientation afterward.
8. Result: Orientation is not preserved.

The polygon will retain its clockwise orientation only if the rigid motion does not include a reflection. Thus, the statement is sometimes true.

Hope this was helpful.