Question

25 ft.
90 ft.
A shortstop is standing in the base path between second
and third base when she fields the ball. She is 25 feet from
second base and needs to make the throw to first base.
Assuming the field is square, how far does she need to
throw the ball? Round your answer to the nearest tenth.

Answer 1

To find out how far the shortstop needs to throw the ball to first base, we can use the Pythagorean theorem.

The baseball diamond is a square, and the distance between bases is 90 feet. Let's outline the positions:

- The distance from the shortstop to second base is 25 feet.
- Therefore, the distance from the shortstop to third base is \(90 - 25 = 65\) feet.
- The distance from second base to first base is 90 feet.

Now, when the shortstop fields the ball, we can consider the position of the shortstop as a point \(S\), second base as point \(B2\), third base as point \(B3\), and first base as point \(B1\). The coordinates of these points can be considered as:

- Second base (B2) at (0, 0)
- First base (B1) at (90, 0)
- Third base (B3) at (0, 90)
- The shortstop (S), who is 25 feet from B2, would be located at (0, -25).

Now, we need to find the distance from the shortstop \(S(0, -25)\) to first base \(B1(90, 0)\). We can use the distance formula:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Substituting in our coordinates:

\[
d = \sqrt{(90 - 0)^2 + (0 - (-25))^2}
\]

This simplifies to:

\[
d = \sqrt{90^2 + 25^2}
\]
\[
d = \sqrt{8100 + 625}
\]
\[
d = \sqrt{8725}
\]

Calculating this gives:

\[
d \approx 93.3 \text{ feet}
\]

Therefore, the shortstop needs to throw the ball approximately **93.3 feet** to first base.