Let a → ,   b → ,   c → be the position vectors of the vertices of a triangle A…

Let a→, b→, c→ be the position vectors of the vertices of a triangle ABC. Through the vertices, lines are drawn parallel to the sides to form the triangle A'B'C'. Then the centroid of ΔA'B'C' is
  1. a→+b→+c→9
  2. a→+b→+c→6
  3. a→+b→+c→3
  4. 2a→+b→+c→3

Solution

Here, A is mid-point of B'C', B is mid-point of A'C' and  C is mid-point of A'B'.

By mid-point formula

a→=b'→+c'→2, b→=a'→+c'→2, c→=b'→+a'→2

Centroid of triangle ABC, G=a→+b→+c→3=b'→+c'→2+a'→+c'→2+b'→+a'→23=a'→+b'→+c'→3

which is centroid of triangle A'B'C'

Asked in: AP EAMCET 2022 (04 Jul Shift 1)

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