## Problem of the Week

Problem of the Week

This problem is taken from ohiorc.org.

A grasshopper jumps from its position at (

This problem is taken from ohiorc.org.

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*?