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 $= 34$