Question

how far does the catcher throw the ball from home plate to 2nd base? 13.4 ft 16,129 ft 127.3 ft 63.6 ft

Explanation:

To determine the distance from home plate to second base in a baseball diamond, we assume the baseball diamond is a square with side length \( s \). The distance from home to second base is the diagonal of the square. For a square with side length \( s \), the diagonal \( d \) is given by the Pythagorean theorem: \( d = s\sqrt{2} \).

In a standard baseball diamond, the distance between consecutive bases (side length \( s \)) is 90 feet.

Step 1: Identify the side length of the square

The side length \( s \) of the baseball diamond (square) is 90 feet.

Step 2: Calculate the diagonal (distance from home to second base)

Using the formula for the diagonal of a square \( d = s\sqrt{2} \), substitute \( s = 90 \):
\[
d = 90\sqrt{2}
\]
Calculate the numerical value:
\[
90\sqrt{2} \approx 90 \times 1.4142 \approx 127.278
\]
Rounding to a reasonable decimal place, this is approximately 127.3 feet.

Answer:

127.3 ft (corresponding to the option "127.3 ft")