Maximum number of points of intersection of four lines on a plane is :

Options

A. 4
B. 6
C. 8
D. 5

Answer

To find the maximum number of points of intersection of four lines on a plane, we can follow these steps:

### Step 1: Understand the intersection of two lines
When two lines are drawn on a plane, they can intersect at most at one point. Therefore, the maximum number of intersection points for two lines is:
- **Max Intersections for 2 Lines = 1**

### Step 2: Add a third line
When a third line is added to the two lines, it can intersect each of the existing lines at most once. Therefore, the maximum number of intersection points with the addition of the third line is:
- **Max Intersections for 3 Lines = 1 (from the first two lines) + 2 (intersections with each of the two existing lines) = 3**

### Step 3: Add a fourth line
Now, when we add a fourth line, it can intersect each of the three existing lines at most once. Thus, the maximum number of intersection points with the addition of the fourth line is:
- **Max Intersections for 4 Lines = 3 (from the first three lines) + 3 (intersections with each of the three existing lines) = 6**

### Conclusion
Therefore, the maximum number of points of intersection of four lines on a plane is:
- **Answer = 6**

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