Which sequence of transformations produces an image that is not congruent to the original figure? A. A translation of 4 units to
the right followed by a dilation of 2. B. A rotation of 90 degrees clockwise followed by a translation of 2 units to the left. . C. A translation of 3 units to the left followed by a reflection across the y-axis. D. A reflection across the y-axis followed by a rotation of 90 degrees counterclockwise.
A) A translation of 4 units to the right followed by a dilation of 2.
Explanation:
3 of our transformations are called isometries. These are transformations that preserve the size and shape of the original figure; they just change the position or orientation of it. Translations, reflections and rotations are all isometries. We know that isometries preserve congruence, since they maintain the size and shape of the original figure.
A dilation is not an isometry. This is because a dilation changes the size of a figure. Since the new figure will not be the same size as the original, they will not be congruent.
Correct option is A. A translation of 4 units to the right followed by a dilation of 2.
Step-by-step explanation:
In options B, C and D, rotation, translation and reflection takes place. Therefore, they are all congruent to the original figure.
In option A, translation of 4 units to the right followed by a dilation of 2 takes place. So, it changes the size of the original figure and hence it is not congruent to the original figure.
