Math Problem Statement
Solution
To solve this problem, we need to find the new coordinates of square PQRS after rotating it 90° clockwise around the origin. For a 90° clockwise rotation, the transformation of a point becomes .
Let’s determine the coordinates of the points first:
Now, applying the rotation rule :
- Point P (4, 2) becomes
- Point Q (8, 2) becomes
- Point R (8, 6) becomes
- Point S (4, 6) becomes
The new coordinates of the rotated square will be:
You can now plot these points on the graph and connect them to form the image of the square after the 90° clockwise rotation.
Do you want further clarification or details on how I got these points?
Here are 5 related questions to expand your understanding:
- What is the rule for a 90° counterclockwise rotation?
- How do you perform a 180° rotation around the origin?
- What are other common transformations besides rotation?
- Can this same method be applied to non-square shapes?
- How would the result change if we rotated by 270° clockwise instead?
Tip: Always remember to apply the transformation rules carefully, paying attention to signs and coordinate swapping during rotations.
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Math Problem Analysis
Mathematical Concepts
Coordinate Geometry
Rotation
Transformations
Formulas
(x, y) → (y, -x) for 90° clockwise rotation
Theorems
Rotation Theorem
Suitable Grade Level
Grades 8-10