Express as a product of reflections in lines the traslation in the vector whose origin is $(3,2)$ and end $(8,4)$

Question

im reading about Geometric Transformations, and i have a doubt...

Express as a product of reflections in lines the traslation in the vector whose origin is $(3,2)$ and end $(8,4)$

Can i used the formule,, im confused cause the formula is applied for a vector whose origin matches the origin of coordinates..

Answer 1

You need to find the cooridinates of your vector. In general the coorcinates of vector with origin in $P=(p_1, p_2, ...,p_n)$ and end in $R=(r_1,r_2,..., r_n)$ are $$\vec{V}=[r_1-p_1, r_2-p_2, ..., r_n-p_n]$$ Notice, that for the vector with origin in the coordinates origin is $$\vec{V}=[r_1, r_2, ..., r_n]$$