QQuestionMathematics
QuestionMathematics
What is the mapping rule for a 180 -degree rotation about the origin?
A) (x, y) → (-y, x)
B) (x, y) → (-y, -x)
C) (x, y) → (-x, -y)
D) (x, y) → (x, -y)
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Answer
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Step 1:I'll solve this step by step with precise LaTeX formatting:
Step 2:: Understand the Rotation
A 180-degree rotation about the origin means transforming a point $$(x, y)$$ to a new point where the point is rotated exactly halfway around the coordinate plane.
Step 3:: Analyze the Coordinate Transformation
In a 180 -degree rotation: - The point moves to the opposite side of the origin - The distance from the origin remains the same - The coordinates change sign in a specific way
Step 4:: Determine the Mapping Rule
- Change the y-coordinate to its negative: $$-y
- Change the x-coordinate to its negative: -x
Step 5:: Verify the Transformation
The mapping rule will be: $$(x, y) \to (-x, -y)
Step 6:: Confirm the Correct Option
Comparing this to the given options, this matches option C.
Final Answer
C) (x, y) \to (-x, -y)
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