Problem

Suppose a baseball playing field is placed on the coordinate plane, as in Example 1.(a) Fi...

Suppose a baseball playing field is placed on the coordinate plane, as in Example 1.

(a) Find the coordinates of first and third base.
(b) If the left fielder is at the point (50, 325), how far is he from first base?
(c) How far is the left fielder in part (b) from the right fielder, who is at the point (280, 20)?

EXAMPLE 1

In a Cubs game at Wrigley Field, a fielder catches the ball near the right-field corner and throws it to second base. The right-field corner is 353 feet from home plate along the right-field foul line. If the fielder is 5 feet from the outfield wall and 5 feet from the foul line, how far must he throw the ball?

SOLUTION

Imagine that the playing field is placed on the coordinate plane, with home plate at the origin and the right-field foul line along the positive x-axis, as shown in Figure 1 (not to scale).

Since the four bases form a square whose sides measure 90 ft each, second base has coordinates (90, 90). The fielder is located 5 feet from the wall, so his x-coordinate is 353 − 5 = 348. His y-coordinate is 5, since he is 5 feet from the foul line. Therefore the distance he throws is the distance from (348, 5) to (90, 90), which can be found as follows.