Question

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

• A. $(\frac{2}{3},0)$
• B. $(\frac{7}{3},\frac{2}{3})$
• C. $(-\frac{7}{3},\frac{2}{3})$
• D. none of these

Answer 1

Answer: (C)

$(-\frac{7}{3},\frac{2}{3})$

Given combined eq

$(x^2+7xy+2y^2)(y-1)=0$

eq of sides

$y=1$ and pair of lines $x^2+7xy+2y^2=0$

Clearly, from eq of pair of lines we can say one vertex is (0,0) and from $y=1$ we can say y-coordinate of each vertices is $1$

On putting $y=1$ in eq of pair of lines

$x^2+7x+2=0$

if $x_1$ $x_2$ are the roots of above eq

$x_1+x_2=-7$

Centroid G$(\frac{0+x_1+x_2}{3},\frac{0+1+1}{3})$

Centroid G$(-\frac{7}{3},\frac{2}{3})$