Geometry, Please Help!

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

A) 180 degree rotation around A changes point A(x,y) to B(x,-y), changing the sign of the y coordinate of point A

B) 180 degree rotation around B changes point B(x,y) to A(x,-y), changing the sign of the y coordinate of point B

C) 180 degree rotation around the midpoint of AB changes (x,y) to (-x,-y) if the segment AB is a straight line

it changes the signs of both x and y coordinates

D) reflection across AB changes nothing, (x,y) remains (x,y)

E) reflection across perpendicular bisector of AB changes (x,y) to (-x,-y), same as C) above

F) translation by the directed segment AB, changes A(x,y) to pont ((x+c), (x+d)) where B was (c,d)

G) translation by the directed segment BA changes B(x,y) to point ((x+c), (x+d)) where A was (c,d)