Answer:
Explanation:
yle performed two transformations on triangle ABC to obtain the congruent triangle XYZ. Let's analyze each series of transformations to determine which one Lyle most likely used.
A. a translation left and then a dilation with a scale factor of 3:
In this series of transformations, a translation left would shift the triangle horizontally without changing its size or shape. Then, a dilation with a scale factor of 3 would enlarge or shrink the triangle uniformly in all directions. Since we want the triangles to be congruent (meaning they have the same shape and size), this series of transformations is unlikely.
B. a dilation with a scale factor of 2.5 and then a rotation 180˚ counterclockwise:
A dilation with a scale factor of 2.5 would enlarge or shrink the triangle uniformly in all directions. However, a rotation of 180˚ counterclockwise would flip the triangle upside down. These transformations would not result in a congruent triangle.
C. a rotation 90˚ clockwise and then a reflection across the y-axis:
A rotation of 90˚ clockwise would rotate the triangle a quarter turn in a clockwise direction. Then, a reflection across the y-axis would mirror the triangle horizontally. These transformations can result in a congruent triangle if the rotation and reflection are performed correctly. Therefore, this series of transformations is a possibility.
D. a reflection across the x-axis and then a dilation with a scale factor of 0.25:
A reflection across the x-axis would mirror the triangle vertically. Then, a dilation with a scale factor of 0.25 would shrink the triangle uniformly in all directions. This series of transformations can also result in a congruent triangle if the reflection and dilation are performed correctly.
Based on the analysis, it is likely that Lyle used either the series of transformations C or D to obtain the congruent triangle XYZ.