Grasshopper Jump

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?

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The landing point is (2ax, 2by).

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