Question

now try rotating the same line segment around a different point. if we rotate line segment np 180 degrees around point x, where will its image be taken?

Explanation:

Step1: Recall rotation property

A 180 - degree rotation around a point $X$ of a line - segment $NP$ will result in a line - segment where the relative positions of $N$ and $P$ with respect to $X$ are reversed. The new line - segment will be on the opposite side of point $X$ and collinear with the original line - segment and point $X$.

Step2: Analyze options

By visualizing the 180 - degree rotation of line segment $NP$ around point $X$, we can see that the correct image will have the endpoints of the line segment on the opposite side of $X$ such that $X$ is still between the two endpoints of the new line segment and all three points (the two endpoints of the new segment and $X$) are collinear.

Answer:

The option where the new line - segment is on the opposite side of point $X$ and collinear with the original line - segment and point $X$ (the third option if we assume the options are numbered from top - left as 1, top - right as 2, bottom - left as 3, bottom - right as 4).