To find out how far Cassie needs to throw the ball to get it to Gabriel, we can set up a coordinate system.
Let’s place Cassie at the origin at the point (0, 0).
According to the problem:
- Desmond is 3 meters south of Cassie, which places Desmond at (0, -3).
- Desmond is also 4 meters west of Gabriel. Thus, if Desmond is at (0, -3) and he is 4 meters west, Gabriel must be 4 meters east of Desmond.
To find Gabriel’s coordinates:
- Since Desmond is at (0, -3) and he is 4 meters west of Gabriel, we can determine Gabriel's coordinates as follows:
- Moving 4 meters east from (0, -3) gives us Gabriel's coordinates of (4, -3).
Now, we need to find the distance between Cassie (0, 0) and Gabriel (4, -3).
We can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Substituting in Cassie’s coordinates \((0, 0)\) and Gabriel’s coordinates \((4, -3)\):
\[ d = \sqrt{(4 - 0)^2 + (-3 - 0)^2} \] \[ = \sqrt{(4)^2 + (-3)^2} \] \[ = \sqrt{16 + 9} \] \[ = \sqrt{25} \] \[ = 5 \]
Therefore, Cassie needs to throw the ball 5 meters to get it to Gabriel.
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