Question

Apply the transformation M to the polygon with the given vertices. Identify and describe the transformation.

M: (x, y) → (-x, -y)
A(-3, 6), B(-3,1), C(1, 1), D(1,6)

Answer 1

The transformation M: (x, y) → (-x, -y) is a rotation by 180 degrees around the origin which results in a point reflection. The vertices of the polygon are transformed to A'(3, -6), B'(3, -1), C'(-1, -1), and D'(-1, -6).

Step-by-step explanation:

The transformation M: (x, y) → (-x, -y) applied to a polygon flips the polygon over the origin, which is a type of transformation known as a rotation of 180 degrees or a point reflection. Applying this transformation to the given vertices results in new vertices: A'(3, -6), B'(3, -1), C'(-1, -1), and D'(-1, -6). The original polygon is rotated around the origin to a new position, however, the shape and size remain unchanged.