If the vertices of a triangle are (3, – 5), (– 7, 4), (10, –k) and its centroid is (k, – 1), then

If the vertices of a triangle are (3, – 5), (– 7, 4), (10, –k) and its centroid is (k, – 1), then

Dear Student,
Centroid of a triangle=x1+x2+x33,y1+y2+y33
k,-1=3-7+103,-5+4-k3On comparing x and y we have,k=3-7+103 or -1=-5+4-k33k=10-4 or -3=-1-k3k=6k=63=2 or k=2So k=2 Regards

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