I bought new monitor that run with G-sync but my gtx 1070 only has HDMI connectors will the G-sync work with an Displayport to HDMI adapater?(active or passive if there a difference between them using one monitor)
Hard to believe any 1070 models are equipped with only HDMI given that Gsync and Displayport are one of the main features. A graphics card bought new will have their ports covered with covers similar to this picture. If 2nd hand, possibly only HDMI was used and the rest are still covered.
I'm only aware of a single GTX 1070 that only has *one* display port (a very tiny Gigabyte), let alone any with zero. If you don't have DisplayPort ports, I'm nearly certain you don't have a GTX 1070.