Two vertices of a triangle are (1, 2), (3, 5) and its centroid is at the origin. Find the coordinates of the third vertex.
Let the vertex of the triangle be A(1, 2), B(3, 5) and C(x, y)
Let the centroid be D(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
C(x, y) = ( 
, 
)
For given coordinates A(1, 2), B(3, 5) and C(x, y), centroid is,
(0, 0) = 
, 
)
Solving for x and y,
1 + 3 +x =0 and 
= 0
∴ x = -4 and y = -7
Hence, the coordinate of third vertex is C(-4, -7)
2