A figure is transformed into a new figure by being rotated 180 degrees, translated left 6 units, and dilated by a factor of 4. How are the old and new figures related?
a)both congruent and similar
b)congruent but not similar
c)similar but not congruent
d)neither similar and congruent
I think the answer is c because it was dilated by 4 which means that the figure was multiplied by 4. Am i right?
you are correct
To determine how the old and new figures are related, let's break down each transformation step and analyze its effect on congruence and similarity.
1. Rotated 180 degrees: A rotation of 180 degrees preserves congruence since the shape remains the same, but it does not preserve similarity since the angles are reversed.
2. Translated left 6 units: Translation preserves both congruence and similarity because the shape moves without changing its size or shape orientation.
3. Dilated by a factor of 4: Dilation changes the size of the figure but preserves its shape, meaning it is similar but not congruent.
Combining these transformations, the figure undergoes a rotation, translation, and dilation, resulting in a similar figure that is not congruent to the original.
Therefore, the correct answer is c) similar but not congruent.