1.

Two vertices of a triangle ABC are given by A ( 2,3 ) and B ( -2 , 1 ) and its centroid G (1 , 2/3)Find the coordinates of the third vertex C of the triangle ABC.

Answer»

So for a triangle with vertices (X1,Y1);(x2,y2);(x3,y3)

so centroid =( \frac{x1+x2+x3}{3} ,  \frac{y1+y2+y3}{3} )

so here 2,3 and 2, -1 and centroid = 1,2/3

so \frac{2+2+x}{3}=1 ⇒ x = -1

and  \frac{3-1+y}{3}=\frac{2}{3} ⇒ y = 0

so other vertex = (-1 , 0) 


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