Question

Line segment AB is 5 units long and is rotated 180 degrees around a point not on line A’B’. Select all true statements about line segment A’B’.

A. Line segment A’B’ is 5 units long.
B. Line segment A’B’ is parallel to AB.
C. Line segment A’B’ is collinear with AB.
D. Line segment A’B’ is located at the same position as AB after the rotation.

Answer 1

After a 180-degree rotation, line segment A'B' remains 5 units long and becomes parallel to AB but is not collinear with AB nor located in the same position.

Step-by-step explanation:

When a line segment is rotated 180 degrees around a point not on the line, there are some geometric properties that remain unchanged and some that result in a new configuration:

• A. Line segment A'B' is 5 units long. - True, rotations preserve the length of a line segment.
• B. Line segment A'B' is parallel to AB. - True, a 180-degree rotation about a point not on the line will result in the line segment being parallel to its original position.
• C. Line segment A'B' is collinear with AB. - False, they will not be collinear unless the rotation is around the midpoint of AB.
• D. Line segment A'B' is located at the same position as AB after the rotation. - False, a rotation moves the line segment to a new position.

The correct statements regarding line segment A'B' after a 180-degree rotation are that it is 5 units long and parallel to AB.