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.
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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 \(x = -6\).
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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 \(x = -3\).