(on a line)
One way of assigning coordinates to points on a line is as follows. Make the line into a directed line by choosing one direction as the positive direction, running say from x' to x. Take a point O on the line as origin and a point A on the line such that OA is equal to the unit length. If P is any point on the line and OP=x, then x is the coordinate of P in this coordinate system. (Here OP denotes the measure.) The coordinate system on the line is determined by the specified direction of the line, the origin and the given unit of length.