Question

Rectangle ABCD is translated and then reflected to create rectangle A'B'C'D'. Do rectangle ABCD and rectangle A'B'C'D' have the same area?

Justify your answer.
Respond in the space provided.

Answer 1

is there a graph for this that I can see?

Answer 2

Rectangle ABCD and A'B'C'D' do not necessarily have the same area after translation and reflection.

While translation preserves the area, reflection does not guarantee preservation. If the reflection is across a line parallel to one side of the rectangle, the areas will be equal. However, if the reflection is across a line perpendicular to one side, the areas will differ.

The reflection essentially swaps the length and width, altering the product of these dimensions. In conclusion, the area of the rectangles may be equal or differ based on the nature of the reflection, emphasizing the importance of considering specific geometric transformations to determine changes in area