Question

Part A:

Rectangle ABCD is translated and then reflected to create rectangle A’BCD. Do rectangle ABCD and rectangle A’BCD have the same area? Justify your answer.

Please provide a reasoning to explain whether the two rectangles have the same area or not.

Answer 1

The area of rectangle ABCD and rectangle A'BCD is the same.

Step-by-step explanation:

When a rectangle is translated, it is moved to a different position while keeping its size and shape the same. When a rectangle is reflected, it is flipped over a line called the line of reflection. In this case, rectangle ABCD is first translated and then reflected to create rectangle A’BCD.

Since translation and reflection do not change the size or shape of a rectangle, the two rectangles will have the same area. The area of a rectangle is determined by multiplying its length by its width, and this does not change with translation or reflection.

Therefore, rectangle ABCD and rectangle A’BCD have the same area.