To determine which sequence of transformations shows that the quadrilaterals are congruent, we need to analyze each option:
- A: Reflect EFGH across the y-axis and then translate the image 5 units down.
- B: Rotate EFGH 90° clockwise about the origin and then translate the image 5 units down.
- C: Rotate EFGH 90° clockwise about the origin and then translate the image 5 units to the right.
- D: Reflect EFGH across the y-axis and then translate the image 5 units to the right.
For congruence, we must confirm that the resulting coordinates from the transformations precisely match the coordinates of the second quadrilateral.
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Reflection across the y-axis changes the x-coordinates of the points. If a point is at (x, y), it becomes (-x, y).
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Rotation 90° clockwise moves each point according to the rule (x, y) -> (y, -x).
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Translation involves adding/subtracting to the x or y coordinates.
You would need to look at the coordinates of both quadrilaterals before determining which transformation correctly causes congruence.
Without the specific coordinates of the quadrilaterals, I cannot give you the definitive answer. However, generally:
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If quadrilateral EFGH needs to be flipped horizontally (negative x-values) and moved down, then Option A is suitable.
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If rotating EFGH makes it align with the second quadrilateral, then Option B or C could work.
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If flipping horizontally and moving right works, then Option D may be applicable.
Please provide the specific coordinates or drawings of the quadrilaterals so that we can analyze which transformation sequence achieves congruence.
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