Could someone me with this problem and possibly explain? the original image is the one on the bottom left-hand corner

Hey, okay so each quadrant of the plane is 90 degrees. Added all up together, if a circle was drawn with its center being the origin, it would be 360 degrees. 180 degrees is half of 360, and two times 90. So 180 would take up two quadrants.

Now, since the problem states the object was rotated ABOUT THE ORIGIN, you have to account for the position of the entire object within its quadrant, rather than just a single point of the object. So, the original object has points at (-1, -2), (-4, -4), and (-3, -7). Now, the way I usually do a problem like this is that I find the point closest to the origin (in this case, (-1, -2)), and I draw a little imaginary line from that point to the origin. Then, I flip that little line according to what the problem tells me to (in this case, 180 degrees). So my little imaginary line is now from the origin to the point (1, 2) instead of the point (-1, -2). Then I do the same for all the other points.

I hope this helps!!!