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The points A,B,C and D represent the numbers Z 1 ,Z 2 ,Z 3 and Z 4 .ABCD is rhombus;AC=2BD.if Z 2 =2+i ,Z 4 =1-2i,find Z 1 and Z 3

The points A,B,C and D represent the numbers Z1,Z2,Z3 and Z4.ABCD is rhombus;AC=2BD.if  Z2=2+i


,Z4=1-2i,find Z1 and Z3

Grade:12th Pass

3 Answers

Kaushik Kumar
32 Points
8 years ago

B(2,1) , D(1,-2)

Mid Point (3/2,-1/2)

Write Equation of CD in symmetric form 

(x-3/2)/-1/3 = (y+1/2)/-1/3 = r 

here r= +(10)^1/2 , -(10)^1/2

 

A = 3/2 - ((10)^1/2)/3

D = -1/2 + ((10)^1/2)/3


mayank singh
10 Points
8 years ago

z1=-3/2 +i1/2

z3=9/2-i3/2

or vice versa.

Prajwal kr
49 Points
8 years ago

POI of diagonals: (3-i)/2.

Using concept of rotation:

2(0.5+2i)/2z1 + i-3      =   i/2

Solving for Z1

Z1 = -1.5i +5.5

Now, using midpoint formula to get Z3

Z3 + Z1  = 2(3-i)/2

Z3=0.5i-2.5

 

 

 

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