Question

Select all transformations that must take any point A to any point B.

a. Rotation of 180° around A
b. Rotation of 180° around B
c. Rotation of 180° around the midpoint of segment AB
d. Reflection across the line AB
e. Reflection across the perpendicular bisector of segment AB
f. Translation by the directed line segment AB
g. Translation by the directed line segment BA"

Answer 1

To take any point A to point B, a rotation of 180° around the midpoint of AB, a reflection across the perpendicular bisector of AB, and translations by the directed line segment AB or BA are the transformations that must be applied.

Step-by-step explanation:

In mathematics, specifically in geometry, transformations are used to move points and figures in various ways. To take any point A to any point B, certain transformations can be applied. Let's explore the transformations listed in the question:

• Rotation of 180° around A would not necessarily take point A to point B.
• Rotation of 180° around B would not necessarily take point A to point B.
• Rotation of 180° around the midpoint of segment AB will always take point A to point B.
• Reflection across the line AB is not guaranteed to take A to B unless B is on line AB.
• Reflection across the perpendicular bisector of segment AB will always take point A to point B because it reflects across the line that is equidistant from A and B.
• Translation by the directed line segment AB will move point A to point B.
• Translation by the directed line segment BA will also move point A to point B, but in the opposite direction.

Therefore, the correct transformations that must take any point A to any point B are a rotation of 180° around the midpoint of segment AB, reflection across the perpendicular bisector of segment AB, and translations by the directed line segment AB or BA.