Question

Let $S=\{(a,b)a,b\in Z,0\le a,b\le 18\}$. The number of lines in $R^2$ passing through $(0,0)$ and exactly one other point in $S$ is

• A. 16
• B. 22
• C. 28
• D. 32

Answer 1

Answer: (A), (B), (C), (D)

We have,
$S=\{(a,b):a,b\in Z,0\le a,b\le 18\}$
Number of line in $R^2$ passing through $(0,0)$ and one other point in $S$ is $34$.
$(1,17),(2,17),(3,17),...,(18,17)=17$ points
$(17,1),(17,2),(17,3),...,(17,18)=17$ points
$\therefore$ Total number of lines $=34$