Math Problem Statement
Solution
To determine the new coordinates of the vertices after a 90-degree clockwise rotation around the origin, we use the rotation transformation rule for 90 degrees clockwise, which swaps the x and y coordinates and changes the sign of the new y-coordinate. The formula to rotate a point 90 degrees clockwise around the origin is:
Based on the image:
- The original coordinates of are .
- The original coordinates of are .
- The original coordinates of are .
- The original coordinates of are .
Applying the rotation formula:
- after 90 degrees clockwise rotation:
- after 90 degrees clockwise rotation:
- after 90 degrees clockwise rotation:
- after 90 degrees clockwise rotation:
These coordinates are based on the visible grid in the photo and the transformation rules for a 90-degree clockwise rotation.
If you have any further questions or need additional details, feel free to ask! Here are some related questions you might consider:
- What would the coordinates be after a 180-degree rotation?
- How would the coordinates change if the rotation were counterclockwise instead?
- What is the significance of the origin in rotation transformations?
- How does changing the point of rotation affect the outcome of the transformation?
- Can you explain how to determine the rotation matrix for different degrees of rotation?
Tip: To check the accuracy of your rotated coordinates, try plotting the original and transformed points on graph paper or using a digital graphing tool to visualize the transformations.
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Math Problem Analysis
Mathematical Concepts
Coordinate Geometry
Transformations
Formulas
(x', y') = (y, -x) for 90° clockwise rotation
Theorems
Rotation transformation theorem
Suitable Grade Level
Grades 7-9
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