Question

Three baseball players are playing catch. Desmond is 3 meters south of Cassie and 4 meters west of Gabriel. How far does Cassie need to throw the ball to get it to Gabriel?

Answer 1

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.