Question

How many lines are determined by three distinct points?

• A. two
• B. three
• C. one or three
• D. six

Answer 1

The correct option is B three

If the given points in the plane are co-llinear then only one possibility of $1$ line can be drawn.

If the given points in the plane are not co-llinear, we can determine the lines from the below given steps,

To draw a line, we need atleast two points.

So,Choosing two points from the given Three points:${}^3{C}_2=\frac{3!}{2!\times 1!}=3$ (The $3$ in the power represents the given three points and the $2$ in the power represents the chosen two points)

$\therefore$, the number of lines that could be drawn ${=}^3{C}_2=\frac{3!}{2!\times 1!}=3$