How Many Lines are Determined From Three Distinct Points

Q. How Many Lines Are Determined From Three Distinct Points? 

(a)Two 

(b)Three 

(c)One or three

(d)Six

Answer: (b) Three

Explanation: The number of lines determined by three distinct points depends on the degree of separation among the points. If they are equidistant, then there are three lines. 

The first and third points can be used as endpoints for two different lines such that each endpoint is also an intersection point. The second point can also be used as an endpoint for a line such that it is not on the same line as either of the first two points. Thus there are three lines determined by these three points.

Let’s take an example of 3 distinct points A, B, and C. A line needs two points to be drawn. So, a line can be drawn from point A to Point B and from the same point A to another point, C.  Same can be done with point B or Point C as the intersection point. So, the resultant line would be AB, BC, and AC.

There is a formula to get the number of lines from n number of points which is,

Number of lines = n(n-1)/2

Puting 3 as n, we get

Number of lines = 3(3-1)/2

Number of lines = 6/2

Number of lines = 3