Question

If (−2, 1) is the centroid of the triangle having its vertices at (x , 0) (5, −2),  (−8, y), then x, y satisfy the relation

Options

• 3x + 8y = 0

•  3x − 8y = 0

• 8x + 3y = 0

• 8x = 3y

• None of these 

Answer 1

We have to find the unknown co-ordinates.

The co-ordinates of vertices are  A(x , 0) ; B(5,-2) ; C (-8, y) 

The co-ordinate of the centroid is (−2, 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,

`(-2 , 1) = ((x + 5 -8)/3 , (y - 2) /3)`

Compare individual terms on both the sides-

`(x - 3) /3 = -2`

So,

x = -3

Similarly,

`(y - 2) /3 = 1`

So,

y = 5 

It can be observed that (x, y) = (−3, 5) does not satisfy any of the relations 3x + 8y = 0, 3x − 8y = 0, 8x + 3y = 0 or 8x = 3y.