The square is dilated by a factor of 2 to form A'B'C'D'.
Which mean the new square sides will be twice as much as the old square.
Let the side length of the square ABCD = x
∴ The side length of the square A'B'C'D' =2x
∵ The area of the square = (side length)²
Area of ABCD = x²
Area of A'B'C'D'= (2x)² = 4x²
∴ Area of A'B'C'D' : Area of ABCD = 4x² : x² = 4 : 1
