The distance between two points on the coordinate geometry is [tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex].
- The distance between Arthur and Cameron is 45.3 m
- Jamie is closer to Cameron than Arthur
- Arthur is the closest to the soccer ball
From the attachment, we have:
[tex]A = (20,35)[/tex] --- Arthur
[tex]J = (45,20)[/tex] -- Jamie
[tex]C = (65,40)[/tex] --- Cameron
The distance between Arthur and Cameron is:
[tex]AC = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
So, we have:
[tex]AC = \sqrt{(20- 65)^2 + (35 - 40)^2}[/tex]
[tex]AC = \sqrt{2050}[/tex]
[tex]AC = 45.3m[/tex]
Hence, the distance between Arthur and Cameron is 45.3 m
To determine the closest to Cameron, we simply calculate the distance between Cameron and Jamie
[tex]CJ = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
So, we have:
[tex]CJ = \sqrt{(45 - 65)^2 + (20 -40)^2}[/tex]
[tex]CJ = \sqrt{800}[/tex]
[tex]CJ = 28.3m[/tex]
By comparison, 28.3 m is less than 45.3 m.
Hence, Jamie is closer to Cameron than Arthur
Also, we have:
[tex]S=(35,60)[/tex]
To determine the closest to the soccer ball, we simply calculate the distance between each person and the ball using:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
So, we have:
[tex]AS = \sqrt{(20 - 35)^2 + (35 - 60)^2} = \sqrt{850} =29.2[/tex] --- Arthur
[tex]JS = \sqrt{(45 - 35)^2 + (20 - 60)^2} = \sqrt{1700} =41.2[/tex] --- Jamie
[tex]CS = \sqrt{(65 - 35)^2 + (40 - 60)^2} = \sqrt{1300} =36.1[/tex] --- Cameron
By comparing the calculated values, 29,2 is the smallest.
Hence, Arthur is the closest to the soccer ball
Read more about distance at:
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