Lets S= (a, b) a, b Z, 0 a, b, 18 . The number of lines in R² passing through (0,0) and exactly one other point in S is

Step-by-step solution

Line passing through origin will be of the form y = mx and any general point on that line can be given by ( h , mh ) . Now if we take the point as (a, b) with restrictions that a and b both are integers between o and 18 , both included, then there will be 18 18=324 such integral pairs in the complete 18 18 square. We need to select those pairs, which do not have any factor i.e coprime pairs in the given range, such as (1,10),(1,11) , etc. Number of lines will be equal to number of such points in the plane. Number o