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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CENGAGE ENGLISH-COORDINATE SYSTEM-Multiple Correct Answers Type
