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Question

Let A(3, -1) and B(1, 1) be the end points of line segment AB. Let P be the middle point of the line segment AB. Let Q be the point situated at a distance √2 units from P on the perpendicular bisector line of AB. What are the possible coordinates of Q?

This question was previously asked in
NDA 2 2025 GAT Question Paper (14-Sep-2025)
The correct answer is

(2, 1)

After calculating the distance and finding the perpendicular bisector, we find that the coordinates of Q are (2, 1).

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Similar Questions

  1. The equation of the locus of a point equidistant from the points \((a, b)\) and \((c, d)\) is \((a-c)x + (b-d)y + k = 0\). What is the value of \(k\)?
  2. If a variable line passes through the point of intersection of the lines \(x + 2y - 1 = 0\) and \(2x - y - 1 = 0\) and meets the coordinate axes in \(A\) and \(B\), then what is the locus of the mid-point of \(AB\)?
  3. The number of points represented by the equation \(x = 5\) on the \(xy\)-plane is
  4. If p and q are real numbers between 0 and 1 such that the points (p, 1), (1, q), and (0, 0) form an equilateral triangle, then what is (p + q) equal to?

  5. The vertices of a triangle are A(1, 1), B(0, 0), and C(2, 0). The angular bisectors of the triangle meet at P. What are the coordinates of P?


Important Questions from Co-ordinate Geometry

  1. The graphs of the linear equations 4x - 2y = 10 and 4x + ky = 2 intersect at a point (a, 4). The value of k is equal to:

  2. In which ratio the point (-3, p) divides the line segment joining the points (-5, -4) and (-2, 3)?

  3. The area (in sq. units) of the triangle formed by the graphs of 8x + 3y = 24, 2x + 8 = y and the x-axis is:

  4. In which quadrant both abscissa and ordinate are negative?

  5. Find the slope of the line joining the points (3, -4) and (5, 2).

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