Final answer:
Yes, scaled copies of a polygon do represent proportional relationships, with changes in dimensions occurring at a consistent rate. All dimensions, including the area, increase or decrease proportionally to the scaling factor applied.
Step-by-step explanation:
Yes, scaled copies of a polygon represent proportional relationships. This means that when you increase or decrease the size of a polygon (scaling), the dimensions of the polygon change at a consistent rate. For example, if the sides of a rectangle are doubled, the new scaled rectangle will have sides that are all twice as long as the original. This scaling applies to all dimensions of the polygon, including the area, so if one side is doubled, the area will be quadrupled (since area is proportional to the square of the sides, as demonstrated by an area proportional to length squared).
Furthermore, if we consider two polygons where one is a scaled copy of the other and the scaling factor is known, we can establish a formula that describes the proportional relationship: for a given linear dimension, y is proportional to x, or y = kx, where k is the constant scaling factor.