To find out how far the shortstop needs to throw the ball to first base, we can visualize the baseball diamond as a square with bases at each corner.
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The distance from home plate to first base (and similarly from second base to third base) is 90 feet.
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The shortstop is positioned 30 feet from second base, which means she is 60 feet from first base. (Since second to first is also 90 feet, and she is 30 feet back from second base, 90 - 30 = 60 feet.)
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Considering the positions:
- Second Base: (90, 0)
- First Base: (90, 90)
- The shortstop, being 30 feet away from second base, is at (90, -30).
Now we need to find the distance from the point (90, -30) to (0, 90):
Using the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Substituting in our coordinates:
\[ d = \sqrt{(90 - 0)^2 + (-30 - 90)^2} \]
Calculating this:
\[ d = \sqrt{(90)^2 + (-120)^2} \] \[ d = \sqrt{8100 + 14400} \] \[ d = \sqrt{22500} \] \[ d = 150 \text{ feet} \]
Therefore, the shortstop needs to throw the ball approximately 150 feet to first base.
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