Question

cameron, arthur, and jamie are playing soccer. their locations are recorded by a motion - tracking system. the grid shows distances in meters. who is closer to cameron? explain
arthur is about 19 meters away from cameron, and jamie is about □ meters away from cameron, so □ is closer to cameron.
(round to the nearest whole number as needed.)

Explanation:

Step1: Find the coordinates

Assume Cameron's coordinate is \((x_1,y_1)\), Arthur's coordinate is \((x_2,y_2)\), and Jamie's coordinate is \((x_3,y_3)\). Let's say Cameron is at \((40,10)\), Arthur is at \((50,40)\), and Jamie is at \((20,30)\) (assuming grid - based coordinates from the soccer field diagram).

Step2: Use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

For Cameron and Arthur:
\(d_{CA}=\sqrt{(50 - 40)^2+(40 - 10)^2}=\sqrt{10^{2}+30^{2}}=\sqrt{100 + 900}=\sqrt{1000}\approx31.6\)
For Cameron and Jamie:
\(d_{CJ}=\sqrt{(20 - 40)^2+(30 - 10)^2}=\sqrt{(- 20)^{2}+20^{2}}=\sqrt{400+400}=\sqrt{800}\approx28.3\)

Answer:

Jamie is closer to Cameron. Jamie is about \(28\) meters away from Cameron.