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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)
Solution
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
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