Final answer:
After a 180° rotation around the origin, the vertices of triangle XYZ become X'(4, -7), Y'(0, -8), and Z'(-2, 1), which are the negatives of their original coordinates.
Step-by-step explanation:
The student's question involves finding the vertices of a triangle after a rotation transformation. In this case, the transformation is a 180° rotation around the origin. To perform a 180-degree rotation in the coordinate plane, you change the sign of both x and y coordinates of each vertex. Therefore, the new coordinates after the transformation will be the negatives of the original coordinates.
- X'(-4, 7) becomes X'(4, -7)
- Y(0, 8) becomes Y'(0, -8)
- Z(2, -1) becomes Z'(-2, 1)
As a result, the vertices of the triangle after a 180° rotation around the origin are X'(4, -7), Y'(0, -8), and Z'(-2, 1).