Point D is rotated 180 degrees using B as the center. Explain why the image of D must lie on the ray BA.

Answer:
The image of [tex]D[/tex] must lie on the ray [tex]BA[/tex], since ray [tex]BA[/tex] is antiparallel to ray [tex]BD[/tex]. That is, the angle between both rays is 180 degrees.
Step-by-step explanation:
Let be [tex]D'[/tex] the image of [tex]D[/tex] such that [tex]D[/tex] is rotated 180 degrees counterclockwise with [tex]B[/tex] as center of rotation.
[tex]D'[/tex] must lie on the ray [tex]BA[/tex], since ray [tex]BA[/tex] is antiparallel to ray [tex]BD[/tex]. That is, the angle between both rays is 180 degrees.