Question

If the centroid of the triangle formed by (7, x) (y, −6) and (9, 10) is at (6, 3), then (x, y) =

Options

• (4, 5)

•  (5, 4)

• (−5, −2)

• (5, 2)

Answer 1

We have to find the unknown co-ordinates.

The co-ordinates of vertices are  A(7, x) ; B(y , -6) ; C(9,10)

The co-ordinate of the centroid is (6, 3)

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,

`(6,3) = ((y + 7 + 9) /3 , (x-6 +10)/3)`

Compare individual terms on both the sides-

`(x +4)/3 = 3`

So,

x = 5

Similarly,

`(y + 16)/3 = 6`

So,

y = 2