Question

modeling with mathematics the figure shows the positions of three players at a moment of a water polo match. player a throws the ball to player b, who then throws the ball to player c. round all answers to the nearest tenth of a meter. how far did player a throw the ball?

Explanation:

Step1: Recall distance - formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Player A is at $(8,4)$ and Player B is at $(16,8)$.

Step2: Substitute values into formula

Let $(x_1,y_1)=(8,4)$ and $(x_2,y_2)=(16,8)$. Then $d=\sqrt{(16 - 8)^2+(8 - 4)^2}=\sqrt{8^2+4^2}=\sqrt{64 + 16}=\sqrt{80}$.

Step3: Calculate and round

$\sqrt{80}\approx8.9$ (rounded to the nearest tenth).

Answer:

$8.9$