Final answer:
Coordinate geometry is essential for city planning, as seen in the grid systems of streets and avenues in cities like Manhattan. A sample question demonstrated how to find the coordinates of a park's center based on its position relative to the city grid, illustrating a real-world application of coordinate geometry.
Step-by-step explanation:
Coordinate geometry is widely used in real-world applications such as navigation, urban planning, and surveying. For instance, city planners use coordinate geometry to design the layout of streets and avenues, creating a grid system to facilitate navigation and address identification. In Manhattan or Salt Lake City, for example, streets and avenues are arranged in a predictable pattern that corresponds to a coordinate grid, aiding in both planning and finding locations.
Now, let's create a sample question based on this real-world application:
“Imagine you are a city planner for a new residential area. The blocks are laid out in a grid pattern where each block measures 100 meters by 100 meters. If the city designates the bottom left corner of the residential area as the origin point (0,0), and you are asked to plan a park at the center of the 5th block to the right and 3rd block up from the origin, what would be the coordinates of the center of the park? Assume there are no roads separating the blocks.”
Here's how you solve the question: To find the coordinates of the center of the park, you need to calculate the midpoint of the block located at the 5th block to the right and 3rd block up. Since each block is 100 meters by 100 meters, the park's center coordinates would be at (5 x 100 + 50, 3 x 100 + 50) or (550, 350).