Question

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? m how far did player b throw the ball? m how far would player a have to throw the ball to throw it to player c directly? m

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Calculate distance of A to B

Player A is at $(8,4)$ and player B is at $(18,7)$. So $x_1 = 8,y_1 = 4,x_2=18,y_2 = 7$.
$d_{AB}=\sqrt{(18 - 8)^2+(7 - 4)^2}=\sqrt{10^2+3^2}=\sqrt{100 + 9}=\sqrt{109}\approx 10.4$ m.

Step3: Calculate distance of B to C

Player B is at $(18,7)$ and player C is at $(24,14)$. So $x_1 = 18,y_1 = 7,x_2=24,y_2 = 14$.
$d_{BC}=\sqrt{(24 - 18)^2+(14 - 7)^2}=\sqrt{6^2+7^2}=\sqrt{36+49}=\sqrt{85}\approx 9.2$ m.

Step4: Calculate distance of A to C

Player A is at $(8,4)$ and player C is at $(24,14)$. So $x_1 = 8,y_1 = 4,x_2=24,y_2 = 14$.
$d_{AC}=\sqrt{(24 - 8)^2+(14 - 4)^2}=\sqrt{16^2+10^2}=\sqrt{256 + 100}=\sqrt{356}\approx 18.9$ m.

Answer:

How far did player A throw the ball? 10.4 m
How far did player B throw the ball? 9.2 m
How far would player A have to throw the ball to throw it to player C directly? 18.9 m