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Ashley Fritz 2022-04-07 Answered
Consider the triangle Δ A B C , which D is the midpoint of segment BC, and let the point G be defined such that ( G D ) = 1 3 ( A D ) . Assuming that z A , z B , z C are the complex numbers representing the points (A, B, C):
a. Find the complex number z G that represents the point G
b. Show that ( C G ) = 2 3 ( C F ) and that F is the midpoint of the segment (AB)
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Answers (1)

Abigailf91er
Answered 2022-04-08 Author has 13 answers
Step 1
Let z 1 , z 2 , z 3 be the points A, B, C. Then it is clear that
D = z 2 + z 3 2
The parametric equation of the line from D to A is
γ ( t ) = z 2 + z 3 2 + t ( z 1 z 2 + z 3 2 )
Therefore G = γ ( 1 3 ) which you can simplify.
For the second part take the midpoint of AB and repeat the calculation. If you get exactly the same answer then you are done.

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