A grasshopper jumps from its position at (x,y), over a proud blade of grass at 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. What are the coordinates of this new point, in terms of a, b, x, and y?
Solution
The landing point is (2a – x, 2b – y).
