Math Problem Statement
Solution
The image shows a rotation task where you're asked to determine the coordinates of point D' after a 90° rotation. The original coordinates of D are given as .
90° Rotation Rule:
- Clockwise: The rule for a 90° clockwise rotation around the origin is .
- Counterclockwise: The rule for a 90° counterclockwise rotation is .
Since the image doesn't specify the direction, I will assume it's counterclockwise, which is most common unless otherwise stated.
Applying the 90° Counterclockwise Rotation to :
Using the rule , we get:
- .
Thus, the coordinates of are , matching the third option.
Would you like more details, or do you have any questions?
Here are 5 related questions:
- How would the coordinates change if the rotation was 90° clockwise?
- What is the effect of a 180° rotation on any point?
- How do you rotate a point 270° counterclockwise?
- Can you apply the rotation rule to point A(4, -1)?
- How does the distance from the origin affect the result of a rotation?
Tip: When rotating points, always pay attention to the direction and whether the rotation is around the origin or another point.
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Math Problem Analysis
Mathematical Concepts
Geometry
Coordinate Geometry
Rotations
Formulas
90° Counterclockwise Rotation: (x, y) → (-y, x)
90° Clockwise Rotation: (x, y) → (y, -x)
Theorems
Rotation Theorem in Geometry
Suitable Grade Level
Grades 8-10
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