Math Problem Statement

What conclusion can you make about the images of 2 parallel lines after a 180° rotation about the origin?

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:

  1. "The image lines will be perpendicular."
    Incorrect. Rotating parallel lines does not make them perpendicular.

  2. "They are still parallel because lines remain parallel when rotated."
    Correct. The property of parallelism is maintained after rotation.

  3. "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.

  4. "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:

  1. What happens to the slope of a line after a 180° rotation?
  2. How does the position of two non-parallel lines change after a 180° rotation?
  3. What is the result of rotating a shape with multiple parallel lines by 180°?
  4. Can two parallel lines ever become perpendicular under any rotation?
  5. 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