P=randi(100,10,2) % Example
A=[25 5];
c=bsxfun(@minus,P,A)
[out,idx]=min(hypot(c(:,1),c(:,2)))
% The point is
P(idx,:)
You can check the result
scatter(P(:,1),P(:,2))
hold on
scatter(A(1),A(2),'r')
plot([A(1) P(idx,1)],[A(2), P(idx,2)])
hold off
Another way to do it
P=randi(60,10,2) % Example
A=[25 35];
[pmin,idx]=min(sum(bsxfun(@minus,P,A).^2,2))
% The point is
out=P(idx,:)
