Question

Coordinates for the centroid and two vertices are given, find the third vertex

Answer 1

x1+x2+x3/3= x of centroid of triangle
x1+X2 - x of centroid of trinangle=x3
similarly put value of y1 ,y2,y also like x1,x2,x

Answer 2

U can aasume the third vertex coordinates as (x₃,y₃) and other two vertices as (x₁,y₁) & (x₂,y₂) . The relation between centroid (G) and the vertices of triangle is

$\large\rm\bold{\boxed{G\:=\:(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})}}$

So we have the coordinates of centroid So , we can equate and get the third vertex too .