We can get resolution and stuff for our screen is Screen class. So, we should use Screen.WorkingArea.Width and Screen.WorkingArea.Height, if we want to place something in center of screen.
But, in Windows 8.1 (not sure about other OSs) there is possibility to scale items on screen, if they seem too small. You can check it, by calling context menu on desktop, select "Screen Resolution", and then select "Make text and other items larger or smaller".
And the problem is, that, it seems, it does actually increase screen resolution! So, Screen.WorkingArea.Width and Screen.WorkingArea.Height will give you scaled value, and point Screen.WorkingArea.Width/2 Screen.WorkingArea.Height/2 will no longer in center of actual screen (for 200% scaling this point will be on lower right corner of screen). That might screw a lot of placement of UI items.
So, is it possible to get value of scaling? I can't find any class containing this info.
Most methods to retrieve DPI depends on existing controls, which may be inconvenient sometimes. But DPI can be always retrieved from registry. In C#:
using Microsoft.Win32;
//...
var currentDPI = (int)Registry.GetValue("HKEY_CURRENT_USER\\Control Panel\\Desktop", "LogPixels", 96);
Scale will be
var scale = 96/(float)currentDPI;