Is it possible to prevent drag a image on web site?

Prohibiting the user to download anything from your site is impossible. You don't understand one really basic thing: as soon as some content is rendered on the user's computer, all the content is already there. It's too late to prohibit anything.

Also, even if preventing downloading anything from the site was possible, it would be a pretty brutal violation of the user rights. All the site allows to download content by definition, but may limit its use. The user reasonably expects the same from your site.

Yes, I understand that an image use can violate the copyright of its creator. Such problems are solved by just declaring your and user's right, providing open information on the legal use of the content, and, possibly, by law enforcement (which in practice would be very difficult). Watermarking the image can help protecting it legally.

—SA