JEE Coordinate (6)!

Geometry Level 4

The slopes of three sides of a triangle are -1 , -2 and 3 .

If the orthocenter of this triangle is the origin, and the locus of the centroid of this triangle can be expressed as \( \dfrac xy = \dfrac mn \), where \(m\) and \(n\) are coprime positive integers, find \(m-n\).


This is a part of my set Practice for JEE 2017!
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