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

To determine the maximum number of points of intersection of 4 distinct lines in a plane, let's first consider the following:

Intersection of two lines: Two distinct lines in a plane can intersect at most at one point unless they are parallel (in which case, they do not intersect at all).

Intersection of three lines: Three distinct lines can intersect at most at three points, assuming no two lines are parallel and no three lines are concurrent (i.e., all three lines intersect at different points).

Intersection of four lines: With four distinct lines, we can calculate the maximum number of intersection points by considering how each pair of lines intersects. The maximum number of intersection points occurs when no two lines are parallel and no three lines are concurrent.

The number of ways to choose two lines from four distinct lines to form an intersection is given by the combination formula:

C(n, 2) = n! / (2!(n - 2)!)

For n = 4 (since we have 4 lines), the number of ways to select two lines is:

C(4, 2) = 4! / (2!(4 - 2)!) = (4 × 3) / 2 = 6

Thus, the maximum number of points of intersection of 4 distinct lines in a plane is 6.

Therefore, the correct answer is D. 6.