# Nicholas uses a coordinate system with units of feet to keep track of any items he finds with his metal detector. One day he found a ring at (-2, -6) and a coin at (7, 6). How far apart were the ring and the coin?

1 answer

###### Question:

Nicholas uses a coordinate system with units of feet to keep track of any items he finds with his metal detector. One day he found a ring at (-2, -6) and a coin at (7, 6). How far apart were the ring and the coin?

## Answers

Answer: The distance between the ring and the coin = 15 units.Step-by-step explanation:Distance between two points (a,b) and (c,d) is given by :-[tex]D=\sqrt{(c-a)^2+(d-b)^2}[/tex]Location of rine = (-2,-6)Location of the coin = (7,6)Then, the distance between the ring and the coin [tex]=\sqrt{(6-(-6))^2+(7-(-2))^2}[/tex][tex]=\sqrt{(12)^2+(9)^2}\\\\=\sqrt{144+81}\\\\=\sqrt{225}=15[/tex]Hence, the distance between the ring and the coin = 15 units.

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