Show What You Know: Composition of Transformations
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Question
Quadrilaterals ABCD and EFGH are shown in the coordinate plane.
Quadrilateral EFGH is the image of ABCD after a transformation or sequence of transformations.
Which could be the transformation or sequence of transformations?
Select all that apply.
a translation of 3 units to the right, followed by a reflection across the x-axis
a translation of 3 units to the right, followed by a reflection across the , x, -axis
a rotation of 180° about the origin
a rotation of 180° about the origin
a translation of 12 units downward, followed by a reflection across the y-axis
a translation of 12 units downward, followed by a reflection across the , y, -axis
a reflection across the y-axis, followed by a reflection across the x-axis
a reflection across the , y, -axis, followed by a reflection across the , x, -axis
a reflection across the line with equation y = x
To determine which transformation or sequence of transformations maps quadrilateral ABCD to EFGH, we need to analyze the changes in position, orientation, and shape.
Let's start with the given answer choices:
a translation of 3 units to the right, followed by a reflection across the x-axis:
This means the quadrilateral is shifted 3 units to the right, and then reflected across the x-axis. This transformation does not match the given image.
a rotation of 180° about the origin:
This means the quadrilateral is rotated 180° clockwise or counterclockwise about the origin. This transformation does not match the given image.
a translation of 12 units downward, followed by a reflection across the y-axis:
This means the quadrilateral is shifted 12 units downward and then reflected across the y-axis. This transformation does not match the given image.
a reflection across the y-axis, followed by a reflection across the x-axis:
This means the quadrilateral is first reflected across the y-axis, and then reflected across the x-axis. This transformation yields a valid result.
a reflection across the line with equation y = x:
This means the quadrilateral is reflected across the line y = x. This transformation does not match the given image.
Based on the above analysis, the transformation or sequence of transformations that could result in quadrilateral EFGH is:
- a reflection across the y-axis, followed by a reflection across the x-axis.
Please note that the formatting in the answer choices seems to contain some errors.