QuestionDetermine the transformations to show . Choose all correct options: A) Reflect across , then , then . B) Reflect across . C) Rotate clockwise, then reflect across . D) Rotate , then reflect across . E) Translate units left.
Studdy Solution
STEP 1
Assumptions1. The triangles and \triangleUV are congruent.
. The transformations are performed on .
3. The transformations include reflection across the -axis, reflection across the -axis, rotation around the origin, and translation to the left.
4. The transformations can be performed in any sequence.
STEP 2
We need to determine which sequences of transformations will result in a triangle congruent to \triangleUV.
STEP 3
For option A, reflect across the -axis. Then reflect the image across the -axis. Then reflect the image across the -axis.
STEP 4
Reflecting a figure across the -axis changes the sign of the -coordinates. Reflecting the figure again across the -axis changes the sign of the -coordinates. Reflecting the figure a third time across the -axis changes the sign of the -coordinates again.
STEP 5
The net effect of these three reflections is equivalent to a reflection across the -axis. Therefore, option A is a valid sequence of transformations.
STEP 6
For option B, reflect across the -axis.
STEP 7
Reflecting a figure across the -axis changes the sign of the -coordinates. This transformation alone can result in a triangle congruent to \triangleUV. Therefore, option B is a valid sequence of transformations.
STEP 8
For option C, rotate clockwise around the origin. Then reflect the image across the -axis.
STEP 9
Rotating a figure clockwise around the origin swaps the and -coordinates and changes the sign of the new -coordinates. Reflecting the figure across the -axis changes the sign of the -coordinates.
STEP 10
The net effect of these two transformations is equivalent to a rotation of counterclockwise around the origin. Therefore, option C is not a valid sequence of transformations.
STEP 11
For option D, rotate around the origin. Then reflect the image across the -axis.
STEP 12
Rotating a figure around the origin changes the sign of both the and -coordinates. Reflecting the figure across the -axis changes the sign of the -coordinates.
STEP 13
The net effect of these two transformations is equivalent to a reflection across the -axis. Therefore, option D is a valid sequence of transformations.
STEP 14
For option, translate units to the left.
STEP 15
Translating a figure does not change the shape or size of the figure, only its position. Therefore, option is not a valid sequence of transformations.
The correct sequences of transformations are A, B, and D.
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