Question
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A coordinate plane shows two rectangles A B C D and A double dash B double dash C double dash D double dash. Both the axes range from negative 5 to 5 in unit increments.
Identify a sequence of rigid transformations that would map ABCD→A"B"C"D" . Give your answer in the form of a composition transformation mapping.
(1 point)
Responses
(x,y)→(x,−y−4)
left parenthesis x comma y right parenthesis right arrow left parenthesis x comma minus y negative 4 right parenthesis
(x,y)→(−x−4,y)
left parenthesis x comma y right parenthesis right arrow left parenthesis negative x minus 4 comma y right parenthesis
(x,y)→(x,y+4)
left parenthesis x comma y right parenthesis right arrow left parenthesis x comma y plus 4 right parenthesis
(x,y)→(−x,y−4)
A coordinate plane shows two rectangles A B C D and A double dash B double dash C double dash D double dash. Both the axes range from negative 5 to 5 in unit increments.
Identify a sequence of rigid transformations that would map ABCD→A"B"C"D" . Give your answer in the form of a composition transformation mapping.
(1 point)
Responses
(x,y)→(x,−y−4)
left parenthesis x comma y right parenthesis right arrow left parenthesis x comma minus y negative 4 right parenthesis
(x,y)→(−x−4,y)
left parenthesis x comma y right parenthesis right arrow left parenthesis negative x minus 4 comma y right parenthesis
(x,y)→(x,y+4)
left parenthesis x comma y right parenthesis right arrow left parenthesis x comma y plus 4 right parenthesis
(x,y)→(−x,y−4)
Answers
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Answered by
GPT-4o mini
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.
1. **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.
2. **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.
3. **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. **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.
2. **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.
3. **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)**.
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