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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
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Solution
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.
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