The coordinates on a map for San Francisco are (53, 17) and those for Sacramento are (123, 78). Note that coordinates represent miles. Find the distance between the cities to the nearest mile.
Answer
📍 Coordinate Geometry – Finding the Distance Between Two Cities
🗺️ Step 1: Identify the Coordinates
- San Francisco: (53, 17)
- Sacramento: (123, 78)
Each pair (x, y) represents a point in miles on the map.
📐 Step 2: Use the Distance Formula
The formula to calculate the distance between two points is:
Distance = √[(x₂ − x₁)² + (y₂ − y₁)²]
✏️ Step 3: Plug in the Values
Distance = √[(123 − 53)² + (78 − 17)²]
= √[(70)² + (61)²]
= √[4900 + 3721]
= √[8621] ≈ 92.8 miles
= √[(70)² + (61)²]
= √[4900 + 3721]
= √[8621] ≈ 92.8 miles
✅ Final Answer:
The distance between San Francisco and Sacramento is approximately 93 miles.
💡 Tip: The distance formula is based on the Pythagorean Theorem and is essential for solving coordinate geometry problems in real-world contexts like maps and navigation.