Dear Student, We have to find the unknown co-ordinates. The co-ordinates of vertices are A (3,-5) ; B (-7,4) ; C (10, -k) The co-ordinate of the centroid is (k , - 1) We know that the co-ordinates of the centroid of a triangle whose vertices are `(x_1 ,y_1) ,(x_2 , y_2) ,(x_3 ,y_3)` is- `((x_1 + x_2 + x_3 )/3 , ( y_1 + y_2 + y_3)/ 3)` So, `(k , -1) = ((3-7+10)/3 ,(-5+4-k)/3)` Compare individual terms on both the sides- k = 2 |