Identify the transformation that maps the regular pentagon with a center (0, -2) onto itself.

Solution:

Given,regular pentagon with a center (0, -2).

Definition:

The angle formed by any two consecutive vertices and center of the pentagon measures 72°,

360°/5 = 72°.

So a rotation about the origin, clockwise or counter-clockwise of any other multiples of 72° maps the pentagon to itself.

A regular pentagon has 5 lines of symmetry.

A reflection across any of the 5 lines of symmetry maps the pentagon to itself.

For transformation rotate 144° about the point (0, -2).

Therefore, the transformation 144° maps the regular pentagon with a center (0, -2) onto itself.

Identify the transformation that maps the regular pentagon with a center (0, -2) onto itself.

Summary:

The transformation 144° maps the regular pentagon with a center (0, -2) onto itself.