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?
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
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`