Area-ratio matrix, a new point-set distribution descriptor, is given in the paper, which is an invariance under affine transformation. Based on this, the paper reasoned out why the classic eigenvector approach (EA) matching algorithm has inferior anti-noise ability. To solve the problem, the paper proposesan algorithm of weighted eigenvector point matching algorithm based on area-ratio matrix (WEA-ARM). The algorithm enhances the EA's anti-noise ability, and can match point sets under not only the equilong transformation but also affine transformation. Experiments on both synthetic point sets and real images show the practicability of the algorithm and the correctness of the conclusions in the paper.