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. click the icon to view the soccer field. arthur is about \boxed{} meters (round to the nearest...

Explanation:

Step1: Identify coordinates

Assume grid units are 10m per square. Let's find coordinates:

• Arthur: Let's say (40, 20) (approx from grid)
• Jamie: (10, 45) (approx)
• Cameron: (40, 70) (approx)

Step2: Calculate distance from Cameron to Arthur

Use distance formula $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$
Arthur: (40,20), Cameron: (40,70)
$d_{Arthur-Cameron} = \sqrt{(40 - 40)^2 + (70 - 20)^2} = \sqrt{0 + 2500} = 50$ meters

Step3: Calculate distance from Cameron to Jamie

Jamie: (10,45), Cameron: (40,70)
$d_{Jamie-Cameron} = \sqrt{(40 - 10)^2 + (70 - 45)^2} = \sqrt{900 + 625} = \sqrt{1525} \approx 39.05$ meters

Step4: Compare distances

39.05 < 50, so Jamie is closer. Wait, but the question about Arthur's distance? Wait, maybe I misread. Wait the original question: "Arthur is about [ ] meters..." Wait, maybe the question is distance from Arthur to Cameron? Wait, let's recheck.

Wait, maybe the coordinates: Let's assume each grid square is 10m. Let's get precise coordinates. Let's say:

Arthur: (40, 20) (x=40, y=20)

Cameron: (40, 70) (x=40, y=70)

So vertical distance: 70 - 20 = 50 meters. So Arthur is about 50 meters from Cameron? Wait, but earlier Jamie's distance was ~39, but the question is about Arthur. So maybe the question is "Arthur is about how many meters from Cameron?"

So recalculating Arthur to Cameron:

x1=40, y1=20; x2=40, y2=70.

Distance: $|70 - 20| = 50$ (since x is same, vertical distance). So Arthur is about 50 meters from Cameron.

Answer:

50