Question

cameron, arthur, and jamie are playing soccer. their locations are recorded by a motion tracking system. the distance between gridlines is 5 meters. see examples 3 and 4

1. how far apart are arthur and jamie? round to the nearest tenth of a meter.

Explanation:

Step1: Determine coordinates

Assume each grid - line represents 5 meters. Arthur is at approximately (20, 35) and Jamie is at approximately (50, 25) in grid - based coordinates. In real - world coordinates, Arthur's coordinates are \((20\times5,35\times5)=(100,175)\) and Jamie's coordinates are \((50\times5,25\times5)=(250,125)\).

Step2: Use distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \(x_1 = 100,y_1 = 175,x_2 = 250,y_2 = 125\). Then \(d=\sqrt{(250 - 100)^2+(125 - 175)^2}=\sqrt{150^2+( - 50)^2}=\sqrt{22500 + 2500}=\sqrt{25000}\).

Step3: Calculate and round

\(\sqrt{25000}\approx158.1\) meters.

Answer:

158.1 meters