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On a map's coordinate grid, Ashville is located at (-3,2) and Greensboro is located at...

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schooledmom | Salutatorian

Posted May 9, 2013 at 4:23 PM via web

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On a map's coordinate grid, Ashville is located at (-3,2) and Greensboro is located at (4,8). Hickory is midpoint between Ashville and Greensboro.  What is the approximate distance from ashville to Hickory?

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted May 9, 2013 at 4:45 PM (Answer #1)

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Ashville is located at (-3,2) and Greensboro is located at (4,8).

The distance between two points (x1, y1) and (x2, y2) is D = `sqrt((x2 - x1)^2 + (y2 - y1)^2)`

The distance between Ashville and Greensboro is `sqrt((4 + 3)^2 + (8 - 2)^2)` = `sqrt(49 + 36)` = `sqrt 85`

As Hickory is midpoint between Ashville and Greensboro, the approximate distance from Ashville to Hickory is `sqrt 85/2 ~~ 4.6`

The required distance between Ashville and Hickory is approximately 4.6

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oldnick | Valedictorian

Posted May 10, 2013 at 3:45 AM (Answer #2)

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Another way is to find  Hickory coordinates: Being a Middle point:

`x_H=(x_A+ x_G)/2=3.5`          `y_H=(y_A+y_G)/2=3`

`d(A;H)=d(H:G)=sqrt(x_H ^2+y_H ^2)=` `=sqrt(3.5^2+3^2)=sqrt(21.25)= 4.60`

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