If A (6,3) ,B(-3,5) ,C(4,-2) and D(x,3x) are four points If the ratio of area of triangle DBC and triangle ABC is 1:2 then value of x will be

Dear pallvi

Find the area of triangle ABC

ΔABC =49/2

similerly find the area of triangle DBC

ΔDBC =7|2x-1|

now given ΔDBC/ΔABC   =1/2

  so   7|2x-1|/49/2  = 1/2

       2 |2x-1|/7 =1/2

         |2x-1| =7/4

      2x-1  =±7/4

+ve sign                                             -ve sign

2x-1 = 7/4                                        2x-1 =-7/4

x =11/8                                            x=-3/8

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