Question

consider octagon fghjklmn, where opposite sides of the octagon are parallel.
octagon fghjklmn is rotated 270° clockwise about the origin to form octagon fghjklmn.
part b
which statement is true?
a line - segment fg is parallel to line - segment kj.
b line - segment gh is parallel to line - segment nm.
c line - segment jk is parallel to line - segment ml.
d line - segment kl is parallel to line - segment gf.

Explanation:

Step1: Recall rotation properties

A 270 - degree clock - wise rotation about the origin has a transformation rule \((x,y)\to(y, - x)\). When a figure is rotated, parallel lines remain parallel. In an octagon with opposite sides parallel, we can use the property of rotation to analyze the new parallel relationships.

Step2: Analyze each option

For option A: There is no reason to assume that \(FG'\) is parallel to \(K'J'\) based on the rotation and the original parallel - side property of the octagon.
For option B: Since opposite sides of the original octagon are parallel, and rotation preserves parallelism, and \(GH\) and \(NM\) are opposite sides of the original octagon. After a 270 - degree clock - wise rotation about the origin, the parallel relationship is maintained. So \(G'H'\) is parallel to \(N'M'\).
For option C: There is no basis to claim that \(JK'\) is parallel to \(M'L'\) from the given rotation and original parallel - side information.
For option D: There is no evidence to suggest that \(K'L'\) is parallel to \(G'F'\) from the rotation and the original properties of the octagon.

Answer:

B. Line segment \(G'H'\) is parallel to line segment \(N'M'\)