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]
