Question

If the centroid of the triangle formed by the points (3, −5), (−7, 4), (10, −k) is at the point (k −1), then k =

Options

• 3

• 1

• 2

• 4

Answer 1

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