IP A tennis player moves back and forth along the baseline while waiting for her opponent to serve, producing the position-versus-time graph shown in the figure(Figure 1) .Without performing a calculation, indicate on which of the segments of the graph, A, B, or C, the player has the greatest speed.

ACalculate the player's speed for segment A ?B.Calculate the player's speed for segmentB? C.Calculate the player's speed for segment

A 3UP 2DOWN B(2,1) C(3,3)

To determine the speed of a tennis player at different segments of the graph, we need to calculate the slope of each segment. The slope of a position-versus-time graph represents the player's velocity, which is equivalent to their speed.

Segment A:
To calculate the speed for segment A, we need to find the slope of the line connecting the points A(3,2) and B(3,5). The formula for calculating the slope between two points is:

slope = (change in y-coordinate) / (change in x-coordinate)

In this case, the change in y-coordinate is 5 - 2 = 3, and the change in x-coordinate is 3 - 3 = 0. Since the change in x-coordinate is zero, the slope is undefined. This means that the player's speed during segment A cannot be determined without further information.

Segment B:
To calculate the speed for segment B, we need to find the slope of the line connecting the points B(3,5) and C(4,6). Using the slope formula:

slope = (change in y-coordinate) / (change in x-coordinate)

The change in y-coordinate is 6 - 5 = 1, and the change in x-coordinate is 4 - 3 = 1. Therefore, the slope is 1/1 = 1. This means that the player's speed during segment B is 1.

Segment C:
To calculate the speed for segment C, we need to find the slope of the line connecting the points C(4,6) and D(5,9). Again, using the slope formula:

slope = (change in y-coordinate) / (change in x-coordinate)

The change in y-coordinate is 9 - 6 = 3, and the change in x-coordinate is 5 - 4 = 1. Therefore, the slope is 3/1 = 3. This means that the player's speed during segment C is 3.

So, the answers are:
A. The player's speed during segment A cannot be determined without further information.
B. The player's speed during segment B is 1.
C. The player's speed during segment C is 3.