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Jee Main 2025 — Medium JEE math MCQ

Let \(A(x, y, z)\) be a point in \(xy\)-plane, which is equidistant from three points \((0, 3, 2), (2, 0, 3)\) and \((0, 0, 1)\). Let \(B = (1, 4, -1)\) and \(C = (2, 0, -2)\). Then among the statements (S1) : \(\triangle ABC\) is an isosceles right angled triangle, and (S2) : the area of \(\triangle ABC\) is \(\frac{9\sqrt{2}}{2}\), \[
  1. A. \ \text{both are true} \quad
  2. B. \ \text{only (S2) is true} \quad
  3. C. \ \text{only (S1) is true} \quad
  4. D. \ \text{both are false}. \]

Solution

The correct option is **C**. (C. \ \text{only (S1) is true} \quad)

MATH

medium • PYQ Reworded
Question
Read carefully, then pick the best option.
Let A(x,y,z)A(x, y, z) be a point in xyxy-plane, which is equidistant from three points (0,3,2),(2,0,3)(0, 3, 2), (2, 0, 3) and (0,0,1)(0, 0, 1). Let B=(1,4,−1)B = (1, 4, -1) and C=(2,0,−2)C = (2, 0, -2). Then among the statements (S1) : △ABC\triangle ABC is an isosceles right angled triangle, and (S2) : the area of △ABC\triangle ABC is 922\frac{9\sqrt{2}}{2}, \[
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Jee Main 2025 — Medium JEE Mathematics MCQ | MyGoalPrep