Geo3.6

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Find the centroid of the triangle formed by the lines x^{2}-5xy+4y^{2}=0\, and x+2y-6=0\,

Given pair of lines x^{2}-5xy+4y^{2}=0\,

(x-y)(x-4y)=0\,

Therefore the three sides of the triangle are x=y,x-4y=0,x+2y-6=0\,

Equations 1 and 2 meet at the origin.

Solving 1 and 3, we get A(2,2)\,

Solving 2 and 3,we get B(4,1)\,

Therefore,the centroid of the triangle is \left({\frac  {2+4}{3}},{\frac  {2+1}{3}}\right)\,

The centroid is (2,1)\,


Main Page:Geometry:Straight Lines-II