Question

Jon performs 3 transformations on a pentagon. First, he reflects it over the x-axis. Then, he translates it 3 units to the left and 4 units up. Finally, he reflects the image over the line x = 1. Are the original and transformed images congruent?

A) no; Two reflections will change the size of the original image.

B) no; Reflections and translations are fluid motions. Fluid motions change the size of the original image.

C) yes; Reflections and translations are rigid motions. Rigid motions preserve the size of the original image.

D) yes; Reflections and translations are fluid motions. Fluid motions preserve the size of the original image.
Eliminate

Answer 1

The correct answer is Choice C. The reason these are rigid motions are because when rigid motions occur, the size and shape of the figure doesn't change.

Reflections, translations, and rotations are all rigid motions.

Answer 2

C) Yes; Reflections and translations are rigid motions and rigid motions preserve the size of the original image.

Explanation:

We know that, the two rigid transformations used by Jon are:

1. Reflection which flips the image over a line.

2. Translation which shifts the image in any direction.

Since, both these transformations does not change the size of the original image.

So, options A and B are discarded.

Also, we know that these are rigid transformations i.e. both of them preserves the length of the figure and not fluid transformations which changes the length.

So, option D is discarded.

Hence, option C is correct.