Q. 108 - Precalculus Enhanced with Graphing Utilities

Question

Little League Baseball Refer to Problem 106. Overlay a rectangular coordinate system on a Little League baseball diamond so that the origin is at home plate, the positive

x-axis lies in the direction from home plate to first base, and the positive y-axis lies in the direction from home plate to third base.

(a) What are the coordinates of first base, second base, and third base? Use feet as the unit of measurement.

(b) If the right fielder is located at (180, 20), how far is it from there to second base?

(c) If the center fielder is located at (220, 220), how far is it from there to third base?

Step-by-Step Solution

Answer

(a) Coordinates of first base $\left(60,0\right),$Second base $\left(60,60\right)$ and third base $\left(0,60\right)$

(b) The distance between right fielder and second base is $40\sqrt{10}$

(c) The distance between right fielder and second base is $20\sqrt{185}$

Step 1. Given Information

The positive x-axis lies in the direction from home plate to first base, and the positive y-axis lies in the direction from home plate to third base.

Part (a). Step 1. Finding coordinate of first, second and third base

First base lies 60 feet in the x direction, and 0 feet in the y direction.

Second base lies 60 feet in the x direction, and 60 feet in the y direction.

Third base lies 0 feet in the x direction, and 60 feet in the y direction.

The coordinates are $\left(60,0\right),\left(60,60\right) and \left(0,60\right)$

Part (b). Step 1. Distance between right fielder and second base

$$\begin{gathered} d=\sqrt{{\left(180-60\right)}^2+{\left(20-60\right)}^2} \\ d=40\sqrt{10} \end{gathered}$$

Part (c). Step 1. Distance between centre fielder and third base

$$\begin{gathered} d=\sqrt{{\left(220-0\right)}^2+{\left(220-60\right)}^2} \\ d=20\sqrt{185} \end{gathered}$$