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Thread: cartesian coordinate system, calc change in position

1. cartesian coordinate system, calc change in position

Need to know if an object moved, from x1 to x2, for how much and in which direction
For our case say that y = 0.

examples

Code:
```x1   x2     expected  result
1    -1              -2
1     2                1
-1   -2              -1
-1   -3              -2
6     7                1
7     6               -1
etc```
The simplest way to calc that ?

• Well if y is always zero, then the distance traveled will always be x_final - x_initial. The sign of the answer will tell you whether your moved in the +x direction or the -x direction.

If your y changes, however, you'll have to use the distance formula to calculate the MAGNITUDE of the distance. To get the direction and magnitude, I would use vectors, and their respective operations.

• If both your Y and X coordinates change, you can just use the Pythagorean theorem (a2 + b2 = c2) where the difference in X is your a and the difference in Y is your b. Then solve for c and you have your distance between the two points.

Code:
```Point 1 (-1, 0)
Point 2 (2, 4)

|-1 - 2| = a = 3
|0 - 4| = b = 4

a squared = 9
b squared = 16

9 + 16 = c = 25

The square root of 25 = 5```
The distance between Point 1 and Point 2 is 5.

• Originally Posted by BubikolRamios
Need to know if an object moved, from x1 to x2, for how much and in which direction
For our case say that y = 0.

examples

Code:
```x1   x2     expected  result
1    -1              -2
1     2                1
-1   -2              -1
`-1   -3              -2`
6     7                1
7     6               -1
etc```
The simplest way to calc that ?
deltaX = x2 - x1 where deltaX is the distance moved on the x axis.

Bear in mind that subtracting a negative number is the same as adding the absolute value of that number.

If you take the highlighted xample:

deltaX = x2 - x1 = -3 - (-1) = -3 + 1 = -2

If deltaX is negative (less than 0), the object moved in the negative direction on the x axis. If deltaX is positive, the object moved in the positive direction on the x axis.

If the object moves on the y axis as well, then as bobleny described, you can use Pythagoras' Theorem to solve for the straight line distance between 2 points.

distance = sqrt(deltaX^2 + deltaY^2)

In bobleny's example there needs to be a minor correction

Code:
`9 + 16 = c^2 = 25`

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