Question

cameron, arthur, and jamie are playing soccer. their locations are recorded by a motion tracking system. the grid shows their positions on the soccer field. arthur is about meters away from cameron, and jamie is about meters away from cameron. (round to the nearest whole number as needed.) so is closer to cameron.

Explanation:

Step1: Identify coordinates

Assume each grid - square is 10 meters by 10 meters. Cameron is at about (40, 60), Arthur is at about (30, 20), and Jamie is at about (20, 40).

Step2: Use distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
For Arthur and Cameron: \(x_1 = 30,y_1 = 20,x_2 = 40,y_2 = 60\). Then \(d_{Arthur - Cameron}=\sqrt{(40 - 30)^2+(60 - 20)^2}=\sqrt{10^2 + 40^2}=\sqrt{100+1600}=\sqrt{1700}\approx41.23\approx41\) meters.
For Jamie and Cameron: \(x_1 = 20,y_1 = 40,x_2 = 40,y_2 = 60\). Then \(d_{Jamie - Cameron}=\sqrt{(40 - 20)^2+(60 - 40)^2}=\sqrt{20^2+20^2}=\sqrt{400 + 400}=\sqrt{800}\approx28.28\approx28\) meters.

Answer:

Arthur: 41
Jamie: 28
Jamie