Question

Given the regular polygon, select all of the rotations and reflections that carry the figure onto itself. A polygon with 5 sides. Point d is in the center. Line a is horizontally drawn above point d through 2 vertices. Line b is diagonally drawn from left to right through 1 vertex and the middle of the opposite side. Line c is diagonally drawn from right to left through 1 vertex and the middle of the opposite side. Lines b and c intersect at point d. A. a rotation of 72º around the center, point d B. a reflection across line a, through two vertices C. a reflection across line b, through one vertex, the center d D. a rotation of 60º around the center, point d E. a reflection across line c, and the midpoint of the opposite side

Answer 1

The transformation that will map the polygon onto itself are as follows

A. a rotation of 72º around the center, point d

C. a reflection across line b, through one vertex, the center d

E. a reflection across line c, and the midpoint of the opposite side

How to find the the transformation

The transformation are studied as follows

A regular pentagon has rotational symmetry of 72 degrees

= 360 / 5

= 72

Therefore, rotations of 72 degrees about the center would map onto itself

There are lines of reflective symmetry passing through d and different pairs of vertices.

Lines b and c are diagonal lines through d. The lines have reflective symmetry. Reflections across these lines would preserve the shape.