# Math Help - Coordinate system translation

1. ## Coordinate system translation

Hello everyone. I'm having trouble with what I believe to be a translation issue. Here is the deal.

Say I have a rectangle in 2D space that is define as follows

(.38,.42) (.62,.42)
________________________
|....................................|
|....................................|
|....................................|
|....................................|
|______________________ |
(.38,.58) (.62,.58)

I need to translate it to this system:

(0,0) (1,0)
________________________
|....................................|
|....................................|
|....................................|
|....................................|
|______________________ |
(0,1) (1,1)

The translation has to be somewhat dynamic such that if the rectangle has different dimensions than those listed above, I can still translate to the system (0,0) - (1,1).

If possible, an algebraic solution for x and y would be even better.

I'm totally stumped here, can anyone assist?

2. Originally Posted by dsoltyka
Hello everyone. I'm having trouble with what I believe to be a translation issue. Here is the deal.

Say I have a rectangle in 2D space that is define as follows

(.38,.42) (.62,.42)
________________________
|....................................|
|....................................|
|....................................|
|....................................|
|______________________ |
(.38,.58) (.62,.58)

I need to translate it to this system:

(0,0) (1,0)
________________________
|....................................|
|....................................|
|....................................|
|....................................|
|______________________ |
(0,1) (1,1)

The translation has to be somewhat dynamic such that if the rectangle has different dimensions than those listed above, I can still translate to the system (0,0) - (1,1).

If possible, an algebraic solution for x and y would be even better.

I'm totally stumped here, can anyone assist?
Lets say that the original co-ordinates are (a,c),(b,c),(a,d),(b,d)

where in you question a=.38, b=.62, c=.42,d=.58

and, let x,y be the old co-ordinate axes and X,Y be the new co-ordinate axes

then, the transformation equations are
$X=\frac{x-a}{b-a}$

$Y=\frac{y-c}{d-c}$

3. Forgive my ignorance, but I am unsure how to use those translation formulas to solve my problem.

I'm confused about the numerators of each one. I'm not sure what values to use for the old axis. Can you possibly provide an example of how .38 can become 0 and .62 can become 1? I'd really love to understand this a bit better, thank you.

4. Originally Posted by dsoltyka
Forgive my ignorance, but I am unsure how to use those translation formulas to solve my problem.

I'm confused about the numerators of each one. I'm not sure what values to use for the old axis. Can you possibly provide an example of how .38 can become 0 and .62 can become 1? I'd really love to understand this a bit better, thank you.
the formula I gave

$X=\frac{x-a}{b-a}$

$X=\frac{x-.38}{.62-.38}$
$X=\frac{x-.38}{.24}$
if x=.38,X= $\frac{.38-.38}{.24}$...which is zero.
if x=.62,X= $\frac{.62-.38}{.24}$...which is one.