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The centroid divides each median in the ...

The centroid divides each median in the ……………ratio.

A

1:3

B

1:2

C

2:1

D

0.7:1

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LetA(4,2),B(6,5)andC(1,4)betheverticesof DeltaABC . What do you observe ? Justify the point that divides each median in the ratio. 2:1 is the centroid of a triangle.

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Knowledge Check

  • The centroid of the tetrahedron ABCD divides the line joining the vertex A to the centroid of triangle BCD in the ratio

    A
    " 1: 2 "
    B
    " 2: 1 "
    C
    " 1: 3 "
    D
    " 3: 1 "

  • The theorem applied to divide the line segment in the given ratio is……………

    A
    Pythagorus theorem
    B
    Thales theorem
    C
    Euclid's theorem
    D
    Brahmagupta theorem

  • The centroid of the tetrahedron ABCD divides the line joining the vertex A to the centroid of DeltaABC in the ratio

    A
    `1:2`
    B
    `2:1`
    C
    `1:3`
    D
    `3:1`

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    Define median

    If G is the centroid and AD be a median with length 12 cm of ΔABC, then the value of AG is

    Show that the points O(0,0,0), A(2,-3,3) B(-2,3,-3) are collinear. Find the ratio in which each point divides the segment joining the other two.

    Let A(4,2) , B(6,5) and C(1,4) be the vertices of the △ABC. The median from A meets BC at D. Find the points which divide the line segment BE in the ratio 2 : 1 and also that divide the line segment CF in the ratio 2 : 1 .

    Assertion (A) : If (-1,3,2) and (5,3,2) are respectively the orthocentre and circumcentre of a triangle, then (3,3,2) is its centroid. Reason (R ) : Centroid of the triangle divides the line segment joining the orthocentre and the circumcentre in the ratio 1:2

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