To describe a sequence of transformations, that maps triangle, ABC onto triangle, ABC, a student starts with a reflection over the X axis. How should the student complete the sequence of traffic transformations to Map triangle ABC onto triangle ABC
After reflecting over the X-axis, the student should perform a reflection over the Y-axis to map triangle ABC onto triangle ACB. Then, the student should perform a rotation of 180 degrees about the origin to map triangle ACB onto triangle CBA. Finally, the student should perform a reflection over the line y= -x to map triangle CBA onto triangle ABC. The sequence of transformations is:
1. Reflection over the X-axis
2. Reflection over the Y-axis
3. Rotation of 180 degrees about the origin
4. Reflection over the line y= -x
To complete the sequence of transformations to map triangle ABC onto triangle ABC after a reflection over the X-axis, the student can follow the steps below:
1. Start with the reflection over the X-axis, which means flipping the triangle across the X-axis. This creates a new triangle A'B'C', where A' is the image of A, B' is the image of B, and C' is the image of C.
2. Next, the student needs to translate triangle A'B'C' to an equivalent position as triangle ABC. Translation involves moving the entire triangle without changing its size or orientation. The student should determine the amount and direction of the translation needed to superimpose triangle A'B'C' onto triangle ABC.
3. Finally, the student can perform any necessary rotations or reflections, if required, to completely map triangle A'B'C' onto triangle ABC. Note that rotations can be clockwise or counterclockwise and reflections can be over any axis.
By following these steps, the student will be able to describe the sequence of transformations needed to map triangle ABC onto triangle ABC.