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NDA2022MathematicsThree Dimensional GeometryActual

Consider the points A(2,4,6), B(-2,-4,-2), C(4,6,4) and D(8,14,12) . Which of the following statements is/ are correct? 1. The points are the vertices of a rectangle A B C D . 2. The mid-point of A C is the same as that of B D . Select the correct answer using the code given below :

Options

  1. A1 only
  2. B2 only
  3. CBoth 1 and 2
  4. DNeither 1 nor 2

Correct answer

B. 2 only

Step-by-step solution

aligned & A C= (4-2)^2+(6-4)^2+(4-6)^2 & = 4+4+4 =2 3 & B D= (8+2)^2+(14+4)^2+(12+2)^2 & =2 187 aligned A C B D ( i.e., Diagonals are not equal.) So, statement is wrong. Mid point of A C=(3,5,5) is equal to mid point of B D=(3,5,5) So, statement 2 is correct

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