A reflection over the point (0,0) is given by:
Nevertheless, the reflection is being made over the point (0,-3). We can first make a traslation of the point (0,-3) to the origin. Then, reflect the new coordinates of the point A through the origin and then bring back the new origin to (0,-3).
First, make a traslation such that the new coordinates of (0,-3) are (0,0):
Then, apply a reflection through the origin:
Finally, make a traslation reciprocal to the first one:
Therefore, the reflection over the point (0,-3) can be written as:
Substitute (x,y)=(4,1) to find out the new coordinates of A after the reflection:
Therefore, the coordinates of the point B are (-4,-7).
