How many lines can be drawn to pass through
(i) a given point (ii) two given points (iii) three given points?

Answer

To solve the question of how many lines can be drawn through a given point, two given points, and three given points, we can analyze each scenario step by step.

### Step 1: Lines through a given point
- **Explanation**: When we have a single point, we can draw infinitely many lines through that point. This is because you can draw a line in any direction from that point.
- **Conclusion**: Therefore, the number of lines that can be drawn through a given point is **infinite**.

### Step 2: Lines through two given points
- **Explanation**: When we have two distinct points, there is exactly one straight line that can be drawn through both points. This is a fundamental property of geometry: two points determine a unique line.
- **Conclusion**: Thus, the number of lines that can be drawn through two given points is **1**.

### Step 3: Lines through three given points
- **Explanation**: The number of lines that can be drawn through three points depends on their arrangement:
- If the three points are collinear (i.e., they lie on the same straight line), then there is only **1 line** that can be drawn through all three points.
- If the three points are not collinear, then no single line can pass through all three points simultaneously, meaning the answer would be **0**.
- **Conclusion**: Therefore, the number of lines that can be drawn through three given points is either **1** (if collinear) or **0** (if not collinear).

### Summary of Answers:
- (i) Through a given point: **Infinite**
- (ii) Through two given points: **1**
- (iii) Through three given points: **1** (if collinear) or **0** (if not collinear)