Math Problem Statement
Solution
The question asks about the conclusion regarding the images of two parallel lines after a 180° rotation about the origin. Let’s break this down:
- A 180° rotation essentially turns every point around the origin to the opposite side, but the relative arrangement of parallel lines remains the same.
Analysis of the Answer Choices:
-
"The image lines will be perpendicular."
Incorrect. Rotating parallel lines does not make them perpendicular. -
"They are still parallel because lines remain parallel when rotated."
Correct. The property of parallelism is maintained after rotation. -
"Because the new lines are parallel, they will overlap the original image."
Incorrect. The lines will be parallel but may not overlap unless they pass through the same points. -
"The new lines will have opposite slopes."
Incorrect. The slopes of the lines will indeed change after the rotation, but they remain parallel.
Thus, the correct answer is: "They are still parallel because lines remain parallel when rotated."
Would you like further explanation or details?
Related Questions:
- What happens to the slope of a line after a 180° rotation?
- How does the position of two non-parallel lines change after a 180° rotation?
- What is the result of rotating a shape with multiple parallel lines by 180°?
- Can two parallel lines ever become perpendicular under any rotation?
- How do you calculate the slope of a line after a specific rotation?
Tip:
For any line or shape, rotating it by 180° maintains its basic structure but reverses the direction across the center of rotation.
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Math Problem Analysis
Mathematical Concepts
Geometry
Transformations
Rotation
Formulas
Rotation formula around the origin
Theorems
Properties of parallel lines
Rotation theorem
Suitable Grade Level
Grades 8-10