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).

Answer 1

To find the distance the shortstop needs to throw the ball to first base, we can visualize the baseball diamond as a square. The bases are positioned at the corners of this square.

Let's follow these steps:

1. Understand the layout:

   • Second base and third base are 90 feet apart (the length of each side of the square).
   • The shortstop is 30 feet from second base, which means she is \(90 - 30 = 60\) feet from third base.

2. Determine the coordinates (using a coordinate system):

   • Second base can be considered at the point (90, 0).
   • First base is at (0, 90).
   • The shortstop is 30 feet from second base towards third base, so her position is at (90, -30).

3. Use the distance formula: To find the distance \(d\) from the shortstop to first base: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Here, the coordinates of the shortstop are (90, -30) and those of first base are (0, 90). \[ d = \sqrt{(0 - 90)^2 + (90 - (-30))^2} \] \[ d = \sqrt{(-90)^2 + (90 + 30)^2} \] \[ d = \sqrt{8100 + 14400} \] \[ d = \sqrt{22500} \] \[ d = 150 \]

4. Round to the nearest tenth: Since 150 is already a whole number, the distance the shortstop needs to throw the ball to first base is 150.0 feet.

So, the final answer is 150.0 feet.