Find the third vertex of a triangle, if two of its vertices are at (-3, 1) and (0, -2) and the centroid is at the origin.
Let the vertex of the triangle be A(1, 2), B(3, 5) and C(x, y)
Let the centroid be G(0, 0), as it is given that centroid is given at origin.
We know that centroid of a triangle for (x1 , y1), (x2 , y2) and (x3 , y3) is
G(x, y) = ( 
, 
)
For given coordinates A(1, 2), B(3, 5) and C(x, y), centroid is,
(0, 0) = 
, 
)
Solving for x and y,
-3 +x =0 and 
= 0
∴ x = 3 and y = 1
Hence, the coordinate of third vertex is C(3, 1).
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