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$A(3,2)$ and $B(-2,1)$ are two vertices of a triangle ABC whose centroid G has the coordinates $(5/3,-1/3)$. Find the coordinates of the third vertex C of the triangle.
$A(3,2)$ and $B(-2,1)$ are two vertices of a triangle ABC whose centroid G has the coordinates $(5/3,-1/3)$. Find the coordinates of the third vertex C of the triangle.
CBSE | Class 10 | Co-ordinate Geometry | Exercise 14.4 | Maths | RD Sharma
$A(3,2)$ and $B(-2,1)$ are two vertices of a triangle ABC whose centroid G has the coordinates $(5/3,-1/3)$. Find the coordinates of the third vertex C of the triangle.

The directions of the centroid are just the normal of the directions of the vertices. So to track down the x facilitate of the orthocenter, include the three vertex x organizes and gap by three. Rehash for the y organize.

Assume the coordinates of the third vertex C be (x, y)

Given in the question, $A(3,2)$ and $B(-2,1)$ are two vertices of a triangle ABC

Then, we know that the coordinates of centroid of the triangle are

$\left( \frac{x+3-2}{3},\frac{y+2+1}{3} \right)$

Given in the question that the centroid for the triangle is $(5/3,-1/3)$.

$\frac{x+3-2}{3}=5/3$and $\frac{y+2+1}{3}=-1/3$

$⇒x+1=5⇒y+3=-1$

$⇒x= 4⇒y=-4$

Therefore, the coordinates of the third vertex C is $(4,-4)$

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