The Dixon resultant for a bivariate polynomial system has many interesting properties. When the unmixed canonical bidegree monomial support of the polynomial system undergoes corner cutting, some monomial points become distinguished by being exposed. When a corner has exactly three exposed monomial points, certain rows and columns of the Dixon matrix, called almost-exposed rows and columns, will produce a factor which is a power of the bracket corresponding to the three exposed points. The power is determined by the relative positions of these three exposed points. This observation is very useful when constructing quotient Dixon resultants.