If z1, z2, z3 be the affixes of the vertices A, B and C respectively of a triangle ABC having - Maths - Complex Numbers

Question

If z1, z2, z3 be the affixes of the vertices A, B and C
respectively of a triangle ABC having centroid G Such that z=0 is
the mid point of AG, then Prove that 4z1 + z2 +z3 =0

Lovina Kansal · Accepted Answer

Dear student
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Let the coordinates of A,B  and C be x1,y1,x2,y2 and x3,y3 respectively
Centroid of △ABC=z1+z2+z33Since it is given z=0 is the mid-point of AGi
e z1+z1+z2+z332=0⇒3z1+z1+z2+z36=0⇒4z1+z2+z3=0
â€‹Regards

If z1, z2, z3 be the affixes of the vertices A, B and C respectively of a triangle ABC having centroid G. Such that z=0 is the mid point of AG, then Prove that 4z1 + z2 +z3 =0.