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Question 440004
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Coordinate Geometry Mixed Practice: JEE Main MCQ

Solve this quality-checked JEE multiple-choice question, then review the correct answer and explanation.

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JEE MainHardQuestion 440004

Question

A point moves such that it is equidistant from (3,4) and (1,2). Its locus is:
  1. A
    Perpendicular bisector: x + y = 5
    Correct
  2. B
    Circle
  3. C
    x = y
  4. D
    x + y = 6

Correct answer

Perpendicular bisector: x + y = 5

Explanation

Midpoint of (3,4) and (1,2): (2, 3). Slope of joining line: (4−2)/(3−1) = 1. Perpendicular bisector slope: −1. Equation: y − 3 = −1(x − 2) → y − 3 = −x + 2 → x + y = 5.

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