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NDA 2 2024 Maths, question 58

Topic: Analytical geometry

Q58

If P(2,4)P(2,4), Q(8,12)Q(8,12), R(10,14)R(10,14) and S(x,y)S(x,y) are vertices of a parallelogram, then what is (x+y)(x+y) equal to?

  1. (a) 88
  2. (b) 1010Correct answer
  3. (c) 1212
  4. (d) 1414

Solution.

Answer: (b) 1010

  1. For vertices in the stated consecutive order, opposite diagonals bisect one another, so P+R=Q+S.
  2. Thus S=(2+10−8,4+14−12)=(4,6), giving x+y=10.
  3. The opposite side vectors also agree.