# Math Help - Grid Distances

1. ## Grid Distances

Given a basic X & Y grid what is the formula to determine distance between two grid items?
I.E
First item is at grid 5, 6 second grid item is at 7, 8.

2. Originally Posted by Mystery
Given a basic X & Y grid what is the formula to determine distance between two grid items?
I.E
First item is at grid 5, 6 second grid item is at 7, 8.
It's a form of Pythagoras' Theorem.

For two points $(x_1, y_1)$ and $(x_2,y_2)$ the distance between them (d) is given by:

$d = \sqrt{(y_2-y_1)^2 + (x_2-x_1)^2}$

3. Originally Posted by Mystery
Given a basic X & Y grid what is the formula to determine distance between two grid items?
First item is at grid 5, 6 second grid item is at 7, 8.
No it is not a form of Pythagoras' Theorem.
It is the grid-metric or the 'taxicab' metric.
If $P(x_1,y_1)~\&~Q(x_2,y_2)$ then the grid-metric is $d(P,Q)=\left| {x_1 - x_2 } \right| + \left| {y_1 - y_2 } \right|$

4. what kind of grid is it?