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Three vertices of a triangle ABC are `A(2,1),B(7,1)` and `C(3,4)`. Images of this triangle are taken in x-axis, y-axis and the line `y = x`. If `G_(1),G_(2)` and `G_(3)` are the centroids of the three image triangles then area of triangle `G_(1)G_(2)G_(3)` is equal to

A

10 sq. units

B

20 sq. units

C

25sq. Units

D

30 sq. units

Text Solution

Verified by Experts

The correct Answer is:
B
Centroid of the given triangle `= (4,2)`
So, centroid of the image triangle is itself the image of the original centroid.
`:. G_(1) -= (4,-2), G_(2) -= (-4,2), G_(3) -= (2,4)`
`:.` Area of `DeltaG_(1)G_(2)G_(3)` is `(1)/(2) ||quad{:(4,-2),(-4,2),(2,4),(4,-2):}|| =20` sq. units
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