How to find isometry and functions for the given cartesian equations?

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Catesian question

I am unable to proceed on how to do the steps, if someone can guide me , im not looking for full solution but some guidance.

Question : Denote by a,b the lines with the Cartesian equations y=0,x=0 respectively, and i=[ 1 0 ​ ],j=[ 0 1 ​ ] (a) Find the functions f(x,y) and g(x,y) such that γ a,i ​ (x,y)=(f(x,y),g(x,y)) . (b) If γ a,i ​ (P)=Q , show that the midpoint of the segment PQ belongs to a . (c) What is the isometry γ a,i ​ γ b,j ​

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