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QuestionArt
Which transformation will carry the rectangle shown below onto itself?
A. A reflection over line m
B. A reflection over the line y = 1
C. A rotation 90° counterclockwise about the origin
D. A rotation 270° counterclockwise about the origin
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Answer
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Step 1: Examine the rectangle and consider the effects of each transformation on its position and orientation.
The rectangle is located in the first quadrant and has its top-right vertex at (3, 1) and its bottom-left vertex at (1, 3).
Step 2: Analyze the effect of a reflection over line m.
Without knowing the exact equation of line m, it's hard to determine the exact effect of the reflection. However, if line m is parallel to the y-axis (i.e., a vertical line), a reflection would interchange the x-coordinates of the rectangle's vertices. This would not carry the rectangle onto itself since the vertical position of the vertices would change. If line m is parallel to the x-axis (i.e., a horizontal line), a reflection would interchange the y-coordinates of the rectangle's vertices. Again, this would not carry the rectangle onto itself since the horizontal position of the vertices would change.
Final Answer
None of the provided options (A, B, C, or D) will carry the rectangle onto itself.
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