Final answer:
The correct pre-image statement is that segment mn is located at m (0, 0) and n (2, 0), and is half the length of segment m'n'. By analogy, doubling the side length of a square quadruples its area as seen in Marta's squares with one being twice the side length of the other.
Step-by-step explanation:
The question involves understanding the effect of a dilation transformation on a geometrical figure with respect to length and area.
Segment m'n' with endpoints at m'(^2, -2, 0) and n'(^2, 2, 0) is dilated at a scale factor of 2 from center (2, 0). When dilating at a factor of 2, the length of each segment from the center of dilation is doubled. That means if segment mn is the pre-image, its length should be half the length of segment m'n'. Given that m'n' is located along the x-axis from -2 to 2, it has a length of 4 units. Therefore, segment mn should have a length of 2 units.
Looking at the possible answers, the correct answer is: 1) Segment mn is located at m (0, 0) and n (2, 0) and is half the length of segment m'n'.
To illustrate with a similar problem, Marta's original square has a side length of 4 inches. When the dimensions are doubled, the new side length is 8 inches (twice the original). The area is found by squaring the side length; the original area is 16 square inches (4^2). The larger square then has an area of 64 square inches (8^2), which is four times greater than the area of the smaller square due to the square of the scale factor effect on area.