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Difficulty: 1/102023 NMTC 2023 (QII-28)

How many minimum points are required to draw unique line in plane

Guide / Hint

Hint 1: Recall the postulate: 'Through any two distinct points, there is exactly one straight line.'

Hint 2: How many points do you need to pin down a line so it cannot rotate?

Hint 3: Recall that while a single point allows infinitely many lines to rotate around it, adding a second distinct point pins the line's direction down completely, leaving exactly one unique straight line passing through both.

Solution

Step 1 (Geometric Axiom): According to the fundamental axioms of Euclidean geometry, a unique straight line can be drawn through any two distinct points in a plane.

Step 2 (Analyze minimum points):

  • point is not enough, as infinitely many lines can pass through a single point.

  • distinct points uniquely define exactly line.

Step 3 (Conclusion): The minimum number of points required is exactly 2.

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