The centroid of the triangle whose three sides are given by the combined equation `(x^(2)+7xy+2y^(2))(y-1)=0`, is

Options

A. `(2//3,0)`
B. `(7//3, 2//3)`
C. `(-7//3, 2//3)`
D. none of these

Answer

C

Explanation

The equation of the sides of the triangle are y=1 and `x^(2)+7xy+2y^(2)=0`

Let `A(x_(1),1), B(x_(2),1) and O(0,0)` be the vertices of the triangle. Then `x_(1),x_(2)` are the roots of the eqaution
`x^(2)+7x+2=0`
`therefore" "x_(1)+x_(2)=-7 and x_(1)x_(2)=2`
Thus, the coordinates of the centroid are
`((x_(1)+x_(2)+0)/(3),(1+1+0)/(3))-=(-(7)/(3),(2)/(3))`