A grasshopper jumps from its position at (*x*,*y*) over the point (*a*,*b*) to the point that is diametrically opposite to (*x*,*y*), i.e., the three points are collinear, and the grasshopper’s new position is just as far from (*a*,*b*) as it was before it jumped. What are the coordinates of this new point, in terms of *a*, *b*, *x*, and *y*?

The landing point is (2*a* – *x*, 2*b* – *y*).