Question

What is the maximum number of points of intersection of 4 distinct lines in a plane?
A.2
B.4
C.5
D.6

Answer 1

Hint: We know that, when two lines are intersecting the number points of intersection will never exceed 2. Similarly as the lines are added the points of intersection will definitely increase. So we will use one formula to find the points of intersection if n number of lines are intersected.
Formula used:
If n is the number of lines that are intersected, then the number of points of intersection is given by,
$${\displaystyle \frac{n\left(n-1\right)}{2}}$$

Complete step-by-step answer:
Consider that when two lines are intersected the number of points of intersection is 1 only.
Now if we add one more line then the points of intersection increase from 1 to 3.
Now in the question we have 4 distinct lines. So the number of points of intersection is given by,
$${\displaystyle \frac{n\left(n-1\right)}{2}}$$
$$={\displaystyle \frac{4\left(4-1\right)}{2}}$$
On solving the bracket,
$$={\displaystyle \frac{4\times 3}{2}}$$
On solving the terms we get,
$$=6$$
Thus there is a maximum number of 6 points if 4 distinct lines are intersecting.
So the correct option is D.
So, the correct answer is “Option D”.

Note: Here note that the formula used is obtained from a study. So that we can simply find the number of points of intersection in less time. Otherwise, we need to draw the lines and see the possible cases.