A coordinate plane is placed over an empty lot. You and a friend stand back-to-back at the origin. You face the positive y-axis and your friend faces the negative y-axis. You run 20 feet forward, then 15 feet to your right. At the same time, your friend runs 16 feet forward, then 12 feet to her right. She stops and hits you with a snowball.

We have a coordinate plane that is placed over an empty lot. So you and your friend are set at that coordinate system, so I'll give you the representation of each statement and the distance that the snowball travels from your friend's hand to you.

1. You face the positive y-axis and your friend faces the negative y-axis. 

This statement is represented in Figure 1. So you are the Red square and your friend is the Blue one. The arrows upon the squares mean that you are facing the positive y-axis and your friend the negative one. 

2. You run 20 feet forward, then 15 feet to your right. At the same time, your friend runs 16 feet forward,  then 12 feet to her right.

This is shown in Figure 2. So, at the coordinate system, you move 20 feet upward and 15 feet to your right, that is, you walk from the origin to the point [tex]P_{1}(15,20)[/tex] first moving through the positive y-axis and next through the positive x-axis. On the other hand, your friend moves 16 feet downward and 12 feet to her right, that is, she walks from the origin to the point [tex]P_{2}(-12,-16)[/tex] first moving through the negative y-axis and next through the negative x-axis. 

3. She stops and hits you with a snowball.

This statement is represented in Figure 3. So the snowball has been drawn in gray. The line from your friend to you is the distance the snowball runs.

4. Distance the ball runs.

We can get this answer by using the Distance Formula, that is:

[tex]d=\sqrt{(x_{1}-x_{2})^{2}+(y_{1}-y_{2})^2} \\ d=\sqrt{[15-(-12)]^{2}+[20-(-16)]^2} \\ \boxed{d=45ft}[/tex]