Question

Triangle ABC was transformed to create image ADE. Which transformations show that ABC is similar to ADE?

a) A dilation by a scale factor of 3 and then a translation 3 units up and 4 units left.
b) A dilation by a scale factor of 4/3 and then a translation 3 units up and 4 units left.
c) A dilation by a scale factor of 4/3 and then a 180° rotation about the origin.
d) A dilation by a scale factor of 12 and then a 180° rotation about the origin.

Answer 1

The correct transformations that show Triangle ABC is similar to ADE are a dilation by a scale factor of 4/3 and then a 180° rotation about the origin, as well as a dilation by a scale factor of 12 and then a 180° rotation about the origin.

Step-by-step explanation:

The correct transformations that show Triangle ABC is similar to ADE are:

1. A dilation by a scale factor of 4/3 and then a 180° rotation about the origin.
2. A dilation by a scale factor of 12 and then a 180° rotation about the origin.

Option a) and Option b) involve a translation, which does not preserve similarity. Therefore, options a) and b) are incorrect.

Option c) involves a dilation by a scale factor of 4/3 and a 180° rotation, which preserves similarity. Option d) involves a dilation by a scale factor of 12 and a 180° rotation, which also preserves similarity. Therefore, options c) and d) are the correct transformations that show similarity between Triangle ABC and ADE.