Question

In figure LMNO shown, 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?
A.
x = -4 and x = -6
B.
x = 6 and x = 3
C.
x = 4 and x = 6
D.
x = -6 and x = -3

Answer 1

When the figure LMNO is rotated 90° clockwise about the origin, the coordinates of the points change. The transformation can be described using the following rule:

If a point has coordinates \((x, y)\), after a 90° clockwise rotation around the origin, the new coordinates will be \((y, -x)\).

Given that segments MN and LO are parallel and lie on the lines \(y = 6\) and \(y = 3\), respectively, we can find the new lines after rotation.

1. For the line \(y = 6\):
- Any point on this line can be represented as \((x, 6)\).
- After rotation, the new coordinates will be \((6, -x)\).
- As \(x\) varies, the new y-coordinate will be \(-x\), which translates to a line \(x = -6\).

2. For the line \(y = 3\):
- Any point on this line can be represented as \((x, 3)\).
- After rotation, this point becomes \((3, -x)\).
- As \(x\) varies, this results in a line \(x = -3\).

Thus, after rotation, the segments MN and LO will now be parallel to each other and lie on the lines \(x = -6\) and \(x = -3\).

Therefore, the correct answer is:
**D. \(x = -6\) and \(x = -3\)**.