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Question
If the centroid of the triangle formed by the points (3, −5), (−7, 4), (10, −k) is at the point (k −1), then k =
Options
3
1
2
4
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Solution
We have to find the unknown co-ordinates.
The co-ordinates of vertices are
A (3,-5) ; B (-7,4) ; C (10, -k)
The co-ordinate of the centroid is (k , - 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,
`(k , -1) = ((3-7+10)/3 ,(-5+4-k)/3)`
Compare individual terms on both the sides-
k = 2
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