Final answer:
Transforming point A to point B can be done using specific transformations. Rotations around the midpoint of segment AB, reflections across the perpendicular bisector of segment AB, or translations by the directed line segment AB will result in point A moving to point B.
Step-by-step explanation:
To transform any point A to any point B, certain geometric movements or operations can be applied. It's important to remember that these transformations preserve certain properties of the shape, like distance and angles, while changing its position or orientation.
Let's analyze the given options:
- A) A rotation of 180° around point A will simply spin the plane around point A; it won't move A to B.
- B) Similarly, a rotation of 120° around point B will also spin the plane around point B and won't satisfy the condition.
- C) A rotation of 180° around the midpoint of segment AB will place point A exactly where B is and vice versa. This is a correct transformation.
- D) Reflection across the line AB won't move A to B but rather to a point A' on the opposite side of the line at the same distance.
- E) Reflection across the perpendicular bisector of segment AB will indeed transform A to B, since it's the line equidistant from both A and B.
- F) Translation by the directed line segment AB means sliding the point A by the vector AB, which directly puts A on B.
- G) Translation by the directed line segment BA means moving point A in the opposite direction of B, which would not place A on B.
Therefore, transformations C, E, and F will guarantee that point A transforms to point B.