Solve the following true/false and multiple-choice questions on geometry transformations.

Here are the solutions to your mathematics test questions:

Part I: Write True or False

1. If a point P is translated to point P', then the vector $\vec{PP'}$ is called the translation vector.

   • True. The translation vector defines the direction and magnitude of the shift from the original point to its image.

2. If a point P(2,3) is reflected over the x-axis, then the reflection is P'(2,-3).

   • True. When a point $(x,y)$ is reflected over the x-axis, its image is $(x,-y)$. For P(2,3), the reflection is P'(2,-3).

3. Rotation is a rigid motion but the figures may be turned in the same direction.

   • False. Rotation is indeed a rigid motion (it preserves shape and size), but it changes the orientation of the figure. The phrase "may be turned in the same direction" implies the orientation might not change, which is incorrect for a rotation (unless it's a 0 or 360-degree rotation).

Part II: Choose the best answer

4. Which one's next is the rotation in the counter-clockwise direction?

   • Counter-clockwise rotation is represented by a positive angle.
   • A. $40^\circ$ is a positive angle, indicating a counter-clockwise rotation.
   • B. $-40^\circ$ indicates a clockwise rotation.
   • C. $-100^\circ$ indicates a clockwise rotation.
   • D. $-360^\circ$ indicates a clockwise rotation (a full circle).
   • The correct option is A.

5. If a point P(2,3) is reflected over the y-axis, then the reflection is:

   • When a point $(x,y)$ is reflected over the y-axis, its image is $(-x,y)$.
   • For P(2,3), the reflection over the y-axis is P'(-2,3).
   • A. P'(2,-3) is a reflection over the x-axis.
   • B. P'(-2,3) is a reflection over the y-axis.
   • C. P'(2,3) is the original point.
   • D. All is incorrect.
   • The correct option is B.