You can use the fact that rotation with 360 degrees leaves no effect on the rotated object(assuming point around which rotation was done was constant all the time)
The quadrant in which the image FGH lie is "First quadrant"
How to find the quadrant in which the rotated image lie?
Know that 180 degrees of rotation takes the figure to diagonally opposite quadrant, no matter if it was clockwise or anticlockwise( for 180 degrees, both clockwise and anticlockwise rotation give same result).
It is a fact that rotation with 360 degrees will result in no effect to the figure rotated. It is called full rotation as the point which was rotated 360 degrees, completes full circular path travel and ends up on its previous position.
Since the rotation of the given triangle FGH was done with 1980 degrees rotation, this angle of rotation can be rewritten as
[tex]1980^\circ = 5 \times 360^\circ + 180^\circ[/tex]
Since those 5 times full rotation won't have any effect and the only effect will be of that 180 degrees.
And thus, the triangle will end up in the diagonally opposite quadrant which is 1st quadrant here(as the given figure is in the third quadrant).
Thus,
The quadrant in which the image FGH lie is "First quadrant"
Learn more here about rotation and angles here:
https://brainly.com/question/10060868
