Final answer:
Using the Pythagorean Theorem, the curator's straight-line distance from home to the museum is 10.3 blocks (5150 feet). The area enclosed by the curator's path is 22.5 square blocks, which is the search area for the police.
Step-by-step explanation:
The Pythagorean Theorem provides a method for calculating the distance someone would walk in a city based on a right-angled triangle formed by their route. To find the straight-line distance (the hypotenuse of the triangle) between the starting point and the museum, we use the formula c = √(a² + b²). In this scenario, if the curator walks 9 blocks east and 5 blocks north, the Pythagorean theorem shows that the straight-line path is √(9 blocks)² + (5 blocks)², which equals 10.3 blocks. Each block being 500 feet, this translates to 5150 feet.
To calculate the area of the triangle defined by the curator's walk, we use the formula for the area of a right triangle: A = 1/2 × base × height, where the base and height correspond to the two legs of the walk (9 and 5 blocks). Therefore, the area A = 1/2 × 9 blocks × 5 blocks, which equals 22.5 square blocks. Converting to feet, the area becomes 22.5 × 500² square feet.