Question

The area of triangle RST is 36 square inches. Under which transformation could the area of the image, triangle R'S’T’ not be congruent to the area of the original triangle?

Answer 1

Dilation

Explanation:

There are two main broad types of transformations: rigid and non-rigid. Rigid transformations keep the general shape the same while changing its position, rotation, direction, etc. Non-rigid transformations, on the other hand, may change how big it is.

For the image to have a different area than the original triangle, it would have to be a different size. Therefore, the original triangle must have gone through a non-rigid transformation. The only non-rigid transformation is dilation, so that is the answer.

There is another type of non-rigid transformation called shearing; however, this is fairly uncommon. If you want, you can include that as a possibility in your answer as well or just put "non-rigid transformation."

Let me know if you want more clarification. :)