What coordinate system is this?

[LydiaLi]

I am using 5 data points on Landsat 8 data.

The below two sets of coordinates should be of approximate location (may be off by couple pixels).

What transformation have set 1 undergone? What is the type of coordinate system is used for set 2?

Set 1:

x (lat, east)       y (long, south)
(145.1799927, -38.36000062)
(145.318279, -37.921044)
(145.215016, -37.586101)
(144.5475, -37.79712)
(144.4779, -37.96826)

Set 2:

coor = [(340443.027, -4247447.377),
(352251.003, -4198485.453),
(342211.378, -4161631.039),
(284062.888, -4186258.452),
(278580.779, -4205760.404)]

[DanPatterson]

start with the obvious projections that are used for your area and standard ones like UTM, Web Mercator and any national grids

[BRHolmes]

Lydia,

I do not know the answer for Set 1.  As for Set 2, I apologize if you already know this, but the coordinates listed are UTM coordinates, easting (x-coord) first, then northing (y-coord).  I believe that the northing coordinate is negative because the locations are in the southern hemisphere:

https://www.usgs.gov/faqs/why-do-landsat-scenes-southern-hemisphere-display-negative-utm-values?qt-n... 

Unfortunately, this doesn't help much (at least for me) with the datum of the coordinate system for Set 2.