Question

2 multiple answer 1 point select all transformations that must take any point a to any point b. rotation of 180 degrees around a. rotation of 180 degrees around b. rotation of 180 degrees around the midpoint of segment ab. reflection across the line ab. reflection across the perpendicular bisector of segment ab. translation by the directed line segment ab. translation by the directed line segment ba.

Explanation:

Step1: Analyze rotation around mid - point

A 180 - degree rotation around the mid - point of segment AB will swap the positions of A and B. Let the mid - point of AB be M. The distance AM = BM. A 180 - degree rotation around M will map A to B.

Step2: Analyze translation

A translation by the directed line segment AB moves point A exactly to point B. The length and direction of the directed line segment AB determine the movement from A to B.

Step3: Analyze other options

• Rotation of 180 degrees around A will not move A to B. A stays at A and other points around A are rotated.
• Rotation of 180 degrees around B will not move A to B. B stays at B and other points around B are rotated.
• Reflection across the line AB will not move A to B. Points on the line AB are invariant under reflection across AB.
• Reflection across the perpendicular bisector of segment AB will swap points that are equidistant from the perpendicular bisector, but not necessarily move A to B.
• Translation by the directed line segment BA will move A in the opposite direction of getting to B.

Answer:

Rotation of 180 degrees around the midpoint of segment AB, Translation by the directed line segment AB