Question

In figure LMNO below, segments MN and LO are parallel. The segments lie on the lines y = 6 and y = 3.



If the figure LMNO is rotated 90° clockwise about the origin to create figure L'M'N'O', what lines will the corresponding parallel segments lie on?

Answer 1

When the figure is rotated 90° clockwise about the origin, the x-coordinate of each point becomes its y-coordinate and the y-coordinate of each point becomes the negative of its x-coordinate.

In this case, segment MN lies on the line y = 6, so its endpoint M has coordinates (m, 6) and its endpoint N has coordinates (n, 6).

When the figure is rotated 90° clockwise, M' will have coordinates (6, -m) and N' will have coordinates (6, -n). Therefore, segment M'N' lies on the line x = 6.

Similarly, segment LO lies on the line y = 3, so its endpoint L has coordinates (l, 3) and its endpoint O has coordinates (o, 3).

When the figure is rotated 90° clockwise, L' will have coordinates (3, -l) and O' will have coordinates (3, -o). Therefore, segment L'O' lies on the line x = 3.

So the corresponding parallel segments in figure L'M'N'O' will lie on the lines x = 3 and x = 6.