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JEE Main201815 Apr 2018Morning ShiftMathematicsStraight LinesActual

In a triangle A B C , coordianates of A are (1,2) and the equations of the medians through B and C are x+y=5 and x=4 respectively. Then area of A B C (in sq. units) is

Options

  1. A5
  2. B9
  3. C12
  4. D4

Correct answer

B. 9

Step-by-step solution

Median through C is x=4 So the x coordianate of C is 4 . let C (4, y) , then the midpoint of A(1,2) and C(4, y) is D which lies on the median through B . D ( 1+4 2 , 2+y 2 ) Now 1+4+2+y 2 =5 y=3 . So, C (4,3) . The centroid of the triangle is the intersection of the mesians. Here the medians x=4 and x+4 and x+y=5 intersect at G(4,1) . The area of triangle A B C=3 A G C =3 1 2 [1(1-3)+4(3-2)+4(2-1)]=9 .

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