To determine the sequence of rigid transformations that map rectangle ABCD to rectangle A''B''C''D'', we need to analyze the transformations step by step based on the given transformations.
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Identify Movement: Start by determining how rectangle ABCD is positioned in relation to A''B''C''D''. If A''B''C''D'' is simply a transformation away from ABCD, we consider symmetry and translation.
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Reflect and Translate: If we observe from the description of the rectangles:
- A reflection across a vertical line would turn the rectangle upside down or horizontally.
- A vertical translation would simply move it up or down the coordinate plane.
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Check Options Given:
- (x,y)→(x,−y−4) → This represents a reflection across the x-axis followed by a downward shift (not applicable here).
- (x,y)→(−x−4,y) → This represents a reflection across the y-axis and a leftward shift by 4 units.
- (x,y)→(x,y+4) → This represents an upward shift, which might translate the rectangle.
- (x,y)→(−x,y−4) → This represents a reflection across the y-axis with a downward shift by 4 units.
Given these transformations, the transformation that consistently appears to account for both altering the position and symmetry of rectangles is:
(x,y)→(−x,y−4)
Thus, the final answer that identifies the composition of transformations mapping ABCD to A''B''C''D'' is:
(x,y)→(−x,y−4).
1 answer