Question

As part of a geometric design, Ariel draws a rhombus. She rotates the rhombus 180° around one of its vertices, then dilates the rhombus by a factor of 2. Which describes the relationship between the original rhombus and its image after the rotation and dilation?

A) The image is congruent to the original rhombus.
B) The image is smaller and congruent to the original rhombus.
C) The image is larger and congruent to the original rhombus.
D) The image is a square.

Answer 1

After Ariel rotates the rhombus and dilates it by a factor of 2, the image is larger but maintains the shape of the original rhombus, with all corresponding sides proportional and all angles congruent.

Step-by-step explanation:

When Ariel draws a rhombus and then applies a rotation of 180° around one of its vertices, the rhombus still maintains its original shape and size since a rotation is a rigid motion that preserves distances and angles. However, when she dilates the rhombus by a factor of 2, all sides are doubled in length, resulting in a figure that is larger than the original rhombus but still maintains the shape and all the properties of a rhombus. Hence, the image after rotation and dilation is similar to the original rhombus, meaning that all corresponding angles are congruent and all corresponding sides are in proportion. Therefore, the correct answer to which describes the relationship between the original rhombus and its image after the rotation and dilation is: C) The image is larger and congruent to the original rhombus.