Thread: x-y coordinates in new x-y coordinates

1. x-y coordinates in new x-y coordinates

When I change the x-axis and y-axis of Cartesian System by change the angle from 90 to other angle is there:
(1) Loss information of the figure in the Cartesian System?
(2) link to web page that have computer program that do it?
Thanks,

2. Re: x-y coordinates in new x-y coordinates

I'm not sure exactly what you're asking, but here's how you change coordinates in the plane. I don't know if there's a website or a program on the web to do it for you. The process is pretty simple.

If the points $(1,0)$ and $(0,1)$ in the new coordinates correspond to $(a,b)$ and $(c,d)$ in the old coordinates, then to convert $(x,y)$ to the new coordinates, you have to solve:

$x = ax_n+cy_n$
$y = bx_n+dy_n$

and then $(x_n,y_n)$ is the location in the new coordinates. You will not find a unique solution if $ad-bc$ is zero - this corresponds to the case where one of $(a,b)$ and $(c,d)$ is a multiple of the other.

- Hollywood

3. Re: x-y coordinates in new x-y coordinates

If you rotate the axes by 90 degrees counter-clockwise, the (x, y) becomes (-y, x). There is no "loss of information" because you still have the values of "x" and "y". Also because "rotate 90 degrees clockwise" has the well define inverse "rotate 90 degrees clockwise".

4. Re: x-y coordinates in new x-y coordinates

And how the coordinates x-y will look is I used an x-axis or y-axis or both of them as curve lines?
Can now there will be loss of information?

5. Re: x-y coordinates in new x-y coordinates

Do you mean "if the x and y axes were curves" rather than straight lines? As long as you have the function defining the curves and those functions are "one-to-one and onto", no, there will be no loss of information.