Question

Centroid of triangle divides the median in the ratio of 2:1 from vertex, Find the length of median if distance of centroid from base is 2cm.​

Answer 1

Answer:

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Step-by-step explanation:

Given G is centroid,

AD,BE,CF are median.

To Prove,

GD

AG

=

GE

BG

=

GF

CG

=

1

2

Construction : Produce AD to K such that AG=GK, join BK and CK

Proof : In △ABK,

F and G are mid points of AB and AK respectively

So, FG∥BK [by the mid point therom]

Hence we can say that GC∥BK ..... (A)

In △AKC

Similarly, BG∥KC ..... (B)

By (A) and (B)

BGCK is a parallelogram

In a parallelogram, diagonals bisect each other

So, GD=DK------(C)

AG=GK [By construction]

AG=GD+DK

So, AG=2GD [By (C)]

⇒

GD

AG

=

1

2