When we rotate a figure 90° around a point, we need to check the difference in x and y coordinates between the point and the center of rotation.
Then these differences will swap among themselves.
The difference in x-coordinate between A and B is 1, so now this difference will be the difference in y-coordinate.
The difference in y-coordinate between A and B is 7, so now this difference will be the difference in y-coordinate.
So the coordinates of A'' will be:
[tex]B(-2,-1)\to A^{\doubleprime}(-2+1,-1+7)=A^{\doubleprime}(-1,6)[/tex]Also, the point will be in the third quadrant, so all coordinates are negative:
[tex]A^{\doubleprime}(-1,6)\to A^{\doubleprime}(-1,-6)[/tex]Therefore the answer is C.