is square and the points are collinear if and only if its determinant is zero. Equivalently for three points in a plane, the points are collinear if and only if the slope between one pair of points equals the slope between any other pair of points (in which case the slope between the remaining pair of points will equal the other slopes). By extension, k points in a plane are collinear if and only if any (k–1) pairs of points have the same pairwise slopes. In Euclidean geometry, the Euclidean distance d(a,b) between two points a and b may be used to express the collinearity between three points by: The points a, b and c are collinear if and only if d(x,a) = d(c,a) and d(x,b) = d(c,b) implies x = c. However, there are other notions of distance (such as the Manhattan distance) for which this property is not true. In the geometries where the concept of a line is a primitive notion, as may be the case in some synthetic geometries, other methods of determining collinearity are needed. Types In a sense, all lines in Euclidean geometry are equal, in that, without coordinates, one can not tell them apart from one another. However, lines may play special roles with respect to other objects in the geometry and be divided into types according to that relationship. For instance, with respect to a conic (a circle, ellipse, parabola, or hyperbola), lines can be: tangent lines, which touch the conic at a single point; secant lines, which intersect the conic at two points and pass through its interior; exterior lines, which do not meet the conic at any point of the Euclidean plane; or a directrix, whose distance from a point helps to establish whether the point is on the conic. In the context of determining parallelism in Euclidean geometry, a transversal is a line that intersects two other lines that may or not be parallel to each other. For more general algebraic curves, lines could also be: i-secant lines, meeting the curve in i points counted without multiplicity, or asymptotes, which a curve approaches arbitrarily closely without touching it. With respect to triangles we have: the Euler line, the Simson lines, and central lines. For a convex quadrilateral with at most two parallel sides, the Newton line is the line that connects the midpoints of the two diagonals. For a