A plane figure is bounded by straight lines only. If n is the number of these lines, then the least value of n is :

Options

A. 1
B. 2
C. 3
D. 4

Answer

To determine the least number of straight lines required to bound a plane figure, we can follow these steps:

### Step 1: Understand the concept of bounding a figure
A plane figure is defined as a two-dimensional shape that can be enclosed by straight lines. To bound a figure means to create a closed shape where all points inside are contained within the lines.

**Hint:** Think about how many lines are needed to create a closed shape.

### Step 2: Analyze the number of lines needed
1. **One Line**: A single straight line cannot bound any area, as it extends infinitely in both directions and does not create a closed shape.

**Hint:** Consider what happens if you only have one line.

2. **Two Lines**: Two lines can intersect, but they will still not bound any area because they can only create an angle, leaving an open space.

**Hint:** Visualize two lines intersecting; do they create a closed area?

3. **Three Lines**: When you add a third line, you can create a triangle. A triangle is the simplest polygon that can be formed with straight lines, and it encloses a definite area.

**Hint:** Try drawing three lines to see if they can form a closed shape.

### Step 3: Conclusion
From the analysis, we conclude that at least three lines are necessary to bound a plane figure. Therefore, the least value of \( n \) (the number of lines) is 3.

**Final Answer:** The least value of \( n \) is 3.