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 a. Is this right?

A

A
C
B
A

Anonymous in right 100%

To determine the relationship between the old and new figures, let's break down the transformation step by step:

1. Rotated 180 degrees: This transformation means that the old figure is flipped upside down or turned around by 180 degrees. This does not affect the size of the figure, only its orientation.

2. Translated left 6 units: The figure is moved to the left by 6 units. Translation does not change the shape or size of the figure, only its position.

3. Dilated by a factor of 4: The figure is stretched or expanded by a factor of 4 in all directions. This means that the length, width, and overall size of the figure are increased by a factor of 4.

Considering these three transformations, let's analyze the options:

a) Both congruent and similar: The figure is congruent because the rotation and translation do not change the shape of the figure. It is also similar because dilation preserves the shape but changes the size. Hence, option a) is correct.

b) Congruent but not similar: The figure is congruent because of the rotation and translation, but it is also similar because of the dilation. Hence, this option is incorrect.

c) Similar but not congruent: The figure is indeed similar due to the dilation, but it is also congruent because of the rotation and translation. Thus, this option is incorrect.

d) Neither similar nor congruent: This option does not align with the transformations performed on the figure. As discussed, the figure undergoes both similarity and congruence. Therefore, option d) is incorrect.

So, your initial answer, option a), is indeed correct. The old and new figures are both congruent and similar to each other.