Question

Can any reflection be replaced by a rotation followed by a translation?
1) Yes
2) No

Answer 1

Yes, any reflection can be replaced by a rotation followed by a translation.

Step-by-step explanation:

Yes, any reflection can be replaced by a rotation followed by a translation. This is known as the composition of transformations. In mathematics, a reflection is a transformation that flips a figure across a line, called the line of reflection. A rotation is a transformation that turns a figure about a fixed point, called the center of rotation. A translation is a transformation that slides a figure along a straight line, called the vector of translation.

To replace a reflection with a rotation followed by a translation, follow these steps:

1. Perform a rotation about the center of rotation.
2. Perform a translation along the vector of translation.

By applying these transformations in the correct order, any reflection can be achieved using a rotation followed by a translation.