Math Problem Statement
Solution
From the image you've uploaded, we are looking at a geometric question involving the rotation of a triangle.
In the second image:
- Triangle is rotated about a point , forming a new triangle .
- The question is asking for the relationship between the segments and , given the rotation.
Understanding the options in the first image:
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A. The segments are parallel to each other.
- This would not be correct in the context of rotation. Rotating a figure around a point doesn’t preserve parallelism between corresponding segments.
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B. The segments are perpendicular to each other.
- This might be true only if the rotation is specifically 90°, but it’s not generally true for all rotations.
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C. The segments are congruent to each other.
- This is correct. Rotating a figure preserves the distances between corresponding points, meaning . This property holds for any type of rotation, as rotation is a rigid transformation (it preserves lengths).
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D. The image segment is twice the pre-image segment.
- This would be the case in a dilation transformation, not a rotation.
Conclusion:
The correct answer is C. The segments are congruent to each other, because the distance between a point and the center of rotation remains the same after a rotation.
Would you like more details or have any questions?
Here are 5 related questions for further exploration:
- What are the properties of a rigid transformation?
- How do rotations affect the orientation of a shape?
- What is the difference between rotation and reflection in geometry?
- How does the distance between points change in dilation versus rotation?
- What is the relationship between the angle of rotation and the orientation of segments?
Tip:
In geometry, remember that rotations preserve distances and angles, making them "rigid transformations." This means shapes retain their size and shape after being rotated.
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Math Problem Analysis
Mathematical Concepts
Geometry
Rigid Transformations
Rotation
Formulas
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Theorems
Rotation preserves distances between points (rigid transformation)
Suitable Grade Level
Grades 9-11