1. **State the problem:** We need to find two distances between points X and Y on a grid. - Point X is at the junction of 15th Street and 7th Avenue. - Point Y is at the junction of 21st Street and 4th Avenue. - Streets run east-west, spaced 80 m apart. - Avenues run north-south, spaced 260 m apart. 2. **Calculate the horizontal distance:** - From 7th Avenue to 4th Avenue is a difference of $7 - 4 = 3$ avenues. - Distance horizontally is $3 \times 260 = 780$ meters. 3. **Calculate the vertical distance:** - From 15th Street to 21st Street is a difference of $21 - 15 = 6$ streets. - Distance vertically is $6 \times 80 = 480$ meters. 4. **(a) Straight-line distance (using Pythagoras):** $$d = \sqrt{780^2 + 480^2} = \sqrt{608400 + 230400} = \sqrt{838800}$$ Calculate: $$\sqrt{838800} \approx 916 \text{ meters}$$ 5. **(b) Shortest distance along the roads:** - This is the sum of horizontal and vertical distances: $$780 + 480 = 1260 \text{ meters}$$ **Final answers:** (a) The straight-line distance between point X and point Y is approximately **916 meters**. (b) The shortest distance traveling along the roads is **1260 meters**.