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Let the points A , B , C and D are represented by complex numbers Z 1 , Z 2 , Z 3 and Z 4 respectively. If A , B and C are not collinear and 2 Z 1 + Z 2 + Z 3 - 4 Z 4 = 0 , then the value of A r e a o f Δ D B C A r e a o f Δ A B C is equal to

Correct answer

0.5

Step-by-step solution

Here, Z 4 = Z 1 + Z 2 + Z 3 2 2 Let, midpoint of the line joining B & C is E Z 5 , where Z 5 = Z 2 + Z 3 2 , then Z 4 is midpoint of Z 1 & Z 5 ⇒ A r e a o f Δ B D C A r e a o f Δ B A C = 1 2 = 0 . 5

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