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Difficulty: 1/102023 NMTC 2023 (QI-13)

Total number of lines passing through the point are

Options:

  • A.

    0

  • B.

    1

  • C.

    2

  • infinity

Guide / Hint

Hint 1: How many lines can pass through a single point in a plane?

Hint 2: Can we draw lines of different slopes (like , , etc.) that all pass through ?

Hint 3: Conclude that there are infinitely many lines, corresponding to option index 3.

Solution

Step 1 (Geometric Postulate): Through any single point in a plane, we can draw infinitely many distinct straight lines, each having a different slope.

Step 2 (Apply to the Origin): The point is the origin. Any line of the form (for any real number ) or the vertical line passes through the origin. Since there are infinitely many real numbers , there are infinitely many such lines.

Step 3 (Conclusion): The total number of lines is infinity, which matches option index 3 in ['0', '1', '2', 'infinity'].

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