Question

Three baseball players are playing catch. Herman is 6 meters south of Luca and 8 meters west of valentina. How far does Luca need to throw the ball to get it to Valentina

Answer 1

Luca needs to throw the ball 10 meters to get to Valentina.

Explanation:

Distance Between two Points in the Plane

Let's assume Luca is at the origin of coordinates (0,0).

Since Herman is 6 meters south of Luca, he is located at (0,-8).

We also know Herman is 8 meters west of Valentina, or equivalently, Valentina is 8 meters east of Herman. This locates Valentina at (6,-8).

If Luca wanted to throw the ball to Valentina, he would need to cover the distance between them.

Thus the problem reduces to find the distance between (0,0) and (6,-8).

Given two points A(x,y) and B(w,z), the distance between them is:

`d=√((z-y)^2+(w-x)^2)`

Applying the formula:

`d=√((-8-0)^2+(6-0)^2)`

`d=√((-8)^2+(6)^2)`

`d=√(64+36)=√(100)=10`

d=10 m

Luca needs to throw the ball 10 meters to get to Valentina.