Question

A shortstop is standing in the base path between second and third base when she fields the ball. She is 30 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. (1 point) feet

Answer 1

To calculate the distance the shortstop needs to throw the ball to first base, we can visualize the field as a square with the following bases:

- **Second base (2B)**
- **Third base (3B)**
- **First base (1B)**

Since the bases are typically 90 feet apart in a standard baseball field, we can represent the points on a coordinate plane:

- 2B is at (90, 90)
- 1B is at (90, 0)
- The shortstop is standing between 2B and 3B at a point 30 feet from 2B, which places her at coordinates (90 - 30, 90) = (60, 90).

Now, we can find the distance from this point (60, 90) to first base (90, 0) using the distance formula:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
where
- \((x_1, y_1) = (60, 90)\) (position of the shortstop)
- \((x_2, y_2) = (90, 0)\) (position of 1B)

Substituting the coordinates into the formula:

\[
d = \sqrt{(90 - 60)^2 + (0 - 90)^2}
\]
\[
d = \sqrt{(30)^2 + (-90)^2}
\]
\[
d = \sqrt{900 + 8100}
\]
\[
d = \sqrt{9000}
\]
\[
d \approx 94.868 (rounded)
\]

Rounding to the nearest tenth, the distance she needs to throw the ball to first base is approximately:

\[
\boxed{94.9} \text{ feet.}
\]