To determine the distance the shortstop needs to throw the ball to first base, we first need to define the positions of the bases and get a clear understanding of the situation.
-
The bases on a baseball field are positioned at the corners of a square with each side measuring 90 feet.
-
The coordinates of the bases can be established as follows:
- Home Plate (0, 0)
- First Base (90, 0)
- Second Base (90, 90)
- Third Base (0, 90)
-
The shortstop is positioned between second base and third base, 30 feet from second base. Since second base is at (90, 90), the shortstop’s position can be calculated as:
- The shortstop's distance to third base adds to the coordinates: \(30\) feet away from second base towards third base will position her at (90, 60).
-
We need to find the distance from the shortstop’s position (90, 60) to first base (90, 0).
-
The distance is calculated using the formula for the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\): \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Plugging in the coordinates:
- \(x_1 = 90\), \(y_1 = 60\)
- \(x_2 = 90\), \(y_2 = 0\)
\[ d = \sqrt{(90 - 90)^2 + (0 - 60)^2} = \sqrt{0 + 3600} = \sqrt{3600} = 60 \text{ ft} \]
Therefore, she needs to throw the ball approximately 60 ft to reach first base. Although the options given include 50, 9000, and 94.9, the closest result is approximately 60 ft (which is not listed). If you need to choose from the provided answers, they do not seem to align with the calculated distance accurately.