The park's actual area is 12,000 square meters, with a scale factor of 20 meters to 1 centimeter in the diagram.
To determine the actual area of the park and the scale factor, we can first calculate the distances between the given coordinates and then use the scale of the drawing.
The length of side AB in the diagram is (7 - 2) cm = 5 cm. Using the scale factor of 1 cm to 20 meters, the actual length of AB is 5 cm * 20 meters/cm = 100 meters.
Similarly, the length of side BC is (8 - 2) cm = 6 cm in the diagram, corresponding to an actual length of 6 cm * 20 meters/cm = 120 meters.
The area of the park can be calculated using the lengths of AB and BC as the base and the height of a rectangle, respectively. The area (A) is given by A = base * height = 100 meters * 120 meters = 12,000 square meters.
The scale factor is the ratio of the actual length to the corresponding length on the diagram. For this park, the scale factor is 20 meters (actual length) to 1 centimeter (length on the diagram).
In summary, the actual area of the park is 12,000 square meters, and the scale factor is 20:1 (meters to centimeters).