Question

How many least number of distinct points determine a unique line ?

• A. 3
• B. 2
• C. 1
• D. 4

Hint:

Think about drawing:
With {1 point}, you can draw endless lines through it.
With {2 distinct points}, you can draw only {one} straight line that goes through both. This is a basic rule in geometry: Two points define a unique line.

Answer 1

The Correct Option is B

Concept: This question relates to a fundamental postulate of Euclidean geometry concerning points and lines.

Step 1: Considering one point If you have only one point, an infinite number of different lines can pass through that single point. Imagine a point as a pivot; you can rotate a line around it in all directions. Thus, one point does not determine a unique line.

Step 2: Considering two distinct points If you have two distinct (different) points, there is exactly one straight line that can pass through both of them. You can draw this line by placing a ruler along the two points. Any other line you try to draw that passes through one of these points will not pass through the other if it's a different line. This is often stated as a postulate: "Through any two distinct points, there is exactly one line."

Step 3: Considering three or more points 
If three points are collinear (all lie on the same line), they still determine that same single unique line (defined by any two of them). 
If three points are non-collinear (forming a triangle), no single straight line can pass through all three. Each pair of points will define a different line. The question asks for the "least number" of distinct points to determine a {unique} line.

Step 4: Conclusion The least number of distinct points required to determine a unique straight line is two.