Identify the image of xyz for a composition of a 90 degree rotation and a 180 degree rotation, both about point x.

90° option a

180° option b

Step-by-step explanation: If we do a rotation of 90° about the X point, this means that the angle between the lines XZ and X'Z must be equal to 90°.

The options that have a 90° angle between these two lines are a and c.

And here you can see that, if the rotation is counterclockwise, the option a is a rotation of 90° and option c is a rotation of 270°, while if the rotation is defined clockwise, the option c is 90° and option a is 270°.

Usually, the rotations are defined as counterclockwise, so under this viewpoint, the right answer is option a.

For a 180° rotation the angle between XZ and X'Z' must be equal to 180°, the only option that has a 180° angle is option b, so here b is the answer.