SOLUTION: Overlay a rectangular coordinate system on a Little League baseball diamond so that the origin is at home plate, the positive x-axis lies in the direction from home plate to first

Question 1209079: Overlay a rectangular coordinate system on a Little League baseball diamond so that the origin is at home plate, the positive x-axis lies in the direction from home plate to first base, and the positive y-axis lies in the direction from home plate to third base.
(a) What are the coordinates of first base, second base, and third base? Use feet as the unit of measurement.
(b) If the right fielder is located at (180,20), how far is it from the right fielder to second base?
(c) If the center fielder is located at (220,220), how far is it from the center fielder to third base?
Answer by textot(100) (Show Source): You can put this solution on YOUR website!
**a) Coordinates of Bases**
* **First Base:** (90 feet, 0 feet)
* **Second Base:** (90 feet, 90 feet)
* **Third Base:** (0 feet, 90 feet)
**b) Distance from Right Fielder to Second Base**
* Right Fielder: (180, 20)
* Second Base: (90, 90)
* **Distance Formula:**
* Distance = √[(x2 - x1)² + (y2 - y1)²]
* **Calculate Distance:**
* Distance = √[(90 - 180)² + (90 - 20)²]
* Distance = √[(-90)² + (70)²]
* Distance = √(8100 + 4900)
* Distance = √13000
* Distance ≈ 114 feet
**c) Distance from Center Fielder to Third Base**
* Center Fielder: (220, 220)
* Third Base: (0, 90)
* **Calculate Distance:**
* Distance = √[(0 - 220)² + (90 - 220)²]
* Distance = √[(-220)² + (-130)²]
* Distance = √(48400 + 16900)
* Distance = √65300
* Distance ≈ 255.54 feet
**In summary:**
* **First Base:** (90, 0)
* **Second Base:** (90, 90)
* **Third Base:** (0, 90)
* **Distance from Right Fielder to Second Base:** ≈ 114 feet
* **Distance from Center Fielder to Third Base:** ≈ 255.54 feet

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