Math Problem Statement
Jo uses geometry software to rotate two parallel segments 90° clockwise about the origin. The resultant segments are shown at the right. Which statement is true?
Solution
The question asks about the behavior of two parallel segments after a 90° clockwise rotation about the origin.
In this case, we see the two segments are initially parallel (before rotation). After the 90° clockwise rotation, they remain straight lines but are oriented differently.
Key idea:
- A rotation preserves the relative angles between lines. Therefore, if two lines are parallel before a rotation, they will remain parallel after the rotation, regardless of the angle of rotation.
Answer:
- The correct answer is "The resultant segments are parallel."
Would you like more details on why this happens or have any further questions?
Here are some related questions to consider:
- What is the formula for rotating a point 90° clockwise around the origin?
- What other transformations preserve the parallelism of segments?
- How would the segments look after a 180° rotation instead?
- What happens to the distance between two points after a rotation?
- Can a rotation ever make two non-parallel lines become parallel?
Tip: When lines are rotated, translations or dilations do not change whether they are parallel.
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Math Problem Analysis
Mathematical Concepts
Geometry
Coordinate Geometry
Rotations
Parallel Lines
Formulas
Rotation of a point (x, y) by 90° clockwise: (x', y') = (y, -x)
Theorems
Rotations preserve angles between lines
Parallelism in coordinate geometry
Suitable Grade Level
Grades 8-10