The coordinates of the centroid of the triangle, whose sides are 12×2-20xy+7y2=0 and 2x-3y+4=0 is 83,83.

# The coordinates of the centroid of the triangle, whose sides are $12{x}^{2}-20\mathit{xy}+7{y}^{2}=0$ and $2x-3y+4=0$ is $\left(\frac{8}{3},\frac{8}{3}\right)$.

1. A
True
2. B
False

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### Solution:

$12{x}^{2}-20\mathit{xy}+7{y}^{2}=0$
$⇒\left(6x-7y\right)\left(2x-y\right)=0$

The intersection points of the line 2x−3y+4=0 with pair of straight lines $12{x}^{2}-20\mathit{xy}+7{y}^{2}=0$ are
(1, 2) and (7, 6).
The vertices of the triangle as A(0,0), B(1,2) and C(7,6).
Centroid of triangle ABC is .
Hence, the given statement is true.

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