A double reflection of a preimage across perpendicular lines produces the same result as a 180-degree rotation.
A double reflection of a preimage across perpendicular lines produce the same result as a:(1 point) Responses 180-degree rotation. 180-degree rotation. scaled dilation. scaled dilation. 270-degree rotation. 270-degree rotation. 90-degree rotation.
3 answers
Which explanation for the congruency of the trapezoids is correct? Statement #1: The trapezoids are congruent because ABCD was reflected over the line y=x . Statement #2: The trapezoids are congruent because ABCD was translated left 4 units and up 2 units. Statement #3: The trapezoids are congruent because ABCD was rotated 270° (counterclockwise). Statement #4: The trapezoids are congruent because ABCD was rotated 90° (counterclockwise). (1 point) Statement # is correct.
To determine which statement correctly explains the congruency of the trapezoids, we need to consider the transformations described:
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Reflection over the line y=x: A reflection is a rigid motion and preserves shape and size, so this would result in congruent trapezoids.
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Translation left 4 units and up 2 units: A translation is also a rigid motion, and it preserves the shape and size, resulting in congruent trapezoids.
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Rotation 270° counterclockwise: A rotation is another rigid motion that preserves shape and size, thus resulting in congruent trapezoids.
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Rotation 90° counterclockwise: This is also a rigid motion and preserves congruency.
Since all transformations listed in statements #1, #2, #3, and #4 are rigid transformations that preserve congruency, technically, all of these statements could be considered correct if they lead to congruent trapezoids.
However, if the question asks for only one correct statement, without additional context on the specific trapezoids involved, the general answer is that statements #1, #2, #3, and #4 can all be correct explanations for the congruency of trapezoids.
If you must select only one, and if the context allows you to choose the most common or straightforward method, then statement #1 (reflection) could be a preferred choice. But without context specifying which transformation applies to your situation, it's more reasonable to conclude that any statement could potentially be correct for the congruency of trapezoids derived from different transformations.