Question

for part B how do I find the coordinate for A double prime after the rotation

Answer 1

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:

$B(-2,-1)\to A^{\doubleprime}(-2+1,-1+7)=A^{\doubleprime}(-1,6)$

Also, the point will be in the third quadrant, so all coordinates are negative:

$A^{\doubleprime}(-1,6)\to A^{\doubleprime}(-1,-6)$

Therefore the answer is C.