which of the following is an equivalent transformation to rotation of an object clockwise 90 degrees?

Answer 1

An equivalent transformation to a rotation of an object clockwise 90 degrees can be described in several ways, depending on the context in which you're working. Here are a couple of equivalent transformations:

1. Rotation of -90 degrees Counterclockwise: A rotation of 90 degrees clockwise is equivalent to a rotation of 270 degrees counterclockwise (which is -90 degrees).

2. Reflection followed by Rotation: A transformation can also be achieved through a combination of reflection and rotation. For example, reflecting the object across the line \( y = x \) and then rotating it by 90 degrees.

3. Matrix Representation: In a Cartesian coordinate system, a point \((x, y)\) rotated 90 degrees clockwise can be represented by the transformation: \[ \begin{pmatrix} x' \ y' \end{pmatrix}

   \begin{pmatrix} 0 & 1 \ -1 & 0 \end{pmatrix} \begin{pmatrix} x \ y \end{pmatrix} \] which will give you the new coordinates \((y, -x)\).

If you're considering specific options, please list them, and I can help you identify which one represents an equivalent transformation to the clockwise rotation by 90 degrees.