Question

The vertices of △ XYZ are X(-4,7), Y(0,8) , and Z(2,-1).

What are the vertices of r(180°, (△ XYZ) ？

X' ____Y' _____ Z' _____

Answer 1

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).