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Loss of image quality using Resize

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Paint.NET informs me that my photographic images are 2592 x 1944 pixels with a 72 pixels/inch (28.35 pixels/cm) resolution measuring 36 x 27 inches (91.44 x 68.58 cm). Why is it that printed copies at 15 x 10 centimetres using the File>Print facility directly in Paint.NET are far superior to those using Image>Resize before printing (without saving the resized image)? Is there any means by which I can intervene to resize the image myself without losing the original quality?

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I don't understand. If the print quality is great without using Image->Resize, why would you even bother to invoke Image->Resize?

If you need to change the "print size" of the image, you can do that just by fiddling with the Resolution property (in Image->Resize). "Print Size" is purely a function (in the mathematical sense) of Resolution and Pixel Size. You don't need to resize the image to a new pixel size in order to affect the print size.

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I was simply trying to understand the process. I guess I used to use Resize, thinking that was what I had to do to print on to 15 x 10 cms photo paper, before I discovered that using File>Print did it automatically. If, by using Resize, the Resolution remains the same and I cannot alter that without the size being altered, I guess that means a coarser result on a small sheet of photo paper. But why does using the File>Print facility not result in the same coarser image?

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