point projection on a vector

Hi,
I have a point (Xp,Yp) and a a vector defined by a set of points N, with (Xi,Yi) points where i=1:N.
I want a new point coordinates (Xpn,Ypn) that is the orthogonal projection of (Xp,Yp) on the vector (Xi,Yi).
What is the best and clean way to obtain (Xpn,Ypn)?
I have attached a image as a example.
The line vector (Xi,Yi) is blue.
The point (Xp,Yp) is red.
Best regards.

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