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

(a) 3x + 8y = 0

(b) 3x − 8y = 0

(c) 8x + 3y = 0

(d) 8x = 3y

Answer 1

We have to find the unknown co-ordinates.

The co-ordinates of vertices are

The co-ordinate of the centroid is (−2, 1)

We know that the co-ordinates of the centroid of a triangle whose vertices are is-

So,

Compare individual terms on both the sides-

So,

Similarly,

So,

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.