The points A and C stay fixed because the line that we are using for the reflection is the line that goes from point A to point B
The triangle in Red is the original triangle ABC, the triangle in Blue is the reflected triangle A'B'C' across the line AC
The Point B becomes B', it is "moved" from the top to the bottom of the figure
The point A becomes A' and the point C becomes C', both points remain in the same position, they are "fixed", when we do the reflection across the line AC