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प्रश्न
Two vertices of a triangle have coordinates (−8, 7) and (9, 4) . If the centroid of the triangle is at the origin, what are the coordinates of the third vertex?
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उत्तर
We have to find the co-ordinates of the third vertex of the given triangle. Let the co-ordinates of the third vertex be(x , y) .
The co-ordinates of other two vertices are (−8, 7) and (9, 4)
The co-ordinate of the centroid is (0, 0)
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,
`(0 , 0 ) = ((x - 8 + 9)/3 , (y + 7 + 4) /3)`
Compare individual terms on both the sides-
`(x + 1 ) / 3 = 0`
So,
x= - 1
Similarly,
`(y + 11 ) / 3 = 0`
So,
y = - 11
So the co-ordinate of third vertex ( -1 , - 11 )
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