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NDA 2024 Maths · Mathematics · Straight Lines · easy

If the centroid of the triangle with vertices (1,2), (3,-4) and (x,y) is the origin, then (x,y) is

Single correct option

If the centroid of the triangle with vertices (1,2)(1,2), (3,−4)(3,-4) and (x,y)(x,y) is the origin, then (x,y)(x,y) is
  1. A. (4,−2)(4,-2)
  2. B. (−2,4)(-2,4)
  3. C. (−4,2)(-4,2)
  4. D. (−4,−2)(-4,-2)
Show answer and solution

Answer: (C) (−4,2)(-4,2)

The centroid is the average of the vertices: 1+3+x3=0\frac{1+3+x}{3}=0 gives x=−4x=-4, and 2−4+y3=0\frac{2-4+y}{3}=0 gives y=2y=2. So (x,y)=(−4,2)(x,y)=(-4,2). Trap: (4,−2)(4,-2) comes from forgetting that the sum of coordinates must be zero, so the unknown has the opposite sign of the sum of the known ones; (−2,4)(-2,4) swaps the coordinates.
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