Hello Guest! This is my method of solving this problem:
This is a negative dilation around the point (5.5, 5) with a scale factor of -1/2.
STEP BY STEP EXPLANATION: Let's recall the transformations really quick. There are translations, or movement across a plane. There are reflections, which reflects the given shape over a given axis. There's the identity, which, well, doesn't do anything. There's dilations, which match our given two diagrams!
This might not look like a dilation at first, but you can see it's a negative dilation! If the value of scale factor $k$ is negative, the dilation takes place in the opposite direction from the center of dilation on the same straight line containing the center and the pre-image point.
To find the point which it is dilated around, we can make A and B a rectangle. Just take away the protrution, or just fill in the small rectangle. Now, we need to find the point which is closest to both of the rectangles. And that's (5.5, 5). We also can clearly see the dilation factor is 1/2, but we also know that it is negative. So the factor is -1/2. This is a negative dilation around the point (5.5, 5) with a scale factor of -1/2.
Hope this helped!