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.