The line joining the centroid and the vertices of a triangle divides the triangle in three equal area.

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Draw a triangle and divide it into three triangles of equal area in various ways.

Statement 1: If the vertices of a triangle are having rational coordinates, then its centroid, circumcentre and orthocentre are rational.

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Q. Consider a

△ A B C

in the

x y

-plane with vertices

A = (0, 0), B = (1, 1)

and

C = (9, 1)

. If the line

x = a

divides the triangle into two parts of equal area, then

a

equals:

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