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Geometry ProblemLevel: Mathematics Education, High School, Honors Geometry, College.Click the figure below to see the complete problem 971.
http://imagizer.imageshack.us/v2/800x600q90/835/8nxu.pngDraw rectangular FDNM as per sketchNote that area ( EBC) = area(ENC)And Area(EAF)= area(FME)This problem becomes problem 969.
Let z(P) be the complex number representing P. Let z(C)=0, z(B)=−a, z(E)=−a+bi. Thenz(F) = (−a+bi)(1/2 + √3/2 i) = (−1/2 a − √3/2 b) + (−√3/2 a + 1/2 b)iz(A) = −a + (−√3/2 a + 1/2 b)iz(D) = (−√3/2 a + 1/2 b)iThus BE = b, BC = aAF = −1/2 a + √3/2 b, AE = √3/2 a + 1/2 bDC = √3/2 a − 1/2 b, DF = 1/2 a + √3/2 bArea of ΔEBC = 1/2 abArea of ΔFAE = 1/8 (−√3 a² + 2 ab + √3 b²)Area of ΔFDC = 1/8 (√3 a² + 2 ab − √3 b²)Hence, Area of ΔEBC = Area of ΔFAE + Area of ΔFDC
Sir, can you give me the idea how to get Z(F) Z(B) and Z(D)thx for a lothere is my Gmail account : firstname.lastname@example.org