This paper studies the search directions of three important interior- point algorithms, namely, the primal-affine scaling method, the dual- affine scaling method and the primal-dual interior point method (with logarithmic barrier function). From an algebraic point of view, the paper shows that the search directions of these three algorithms are merely Newton directions along three different ``paths'' that lead to a solution of the Karush-Kuhn-Tucker conditions of a given linear programming problem.