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AP EAMCET201922 Apr 2019Morning ShiftMathematicsThree Dimensional GeometryActual

The points (A(2,-1,4), B(1,0,-1), C(1,2,3) ) and (D(2,1,8) ) form a

Options

  1. Arectangle
  2. Bsquare
  3. Crhombus
  4. Dparallelogram

Correct answer

D. parallelogram

Step-by-step solution

Given points are (A(2,-1,4), B(1,0,-1), C(1,2,3) ) and (D(2,1,8) ). ( A B= 1^2+1^2+5^2 = 27 ) ( aligned & B C= 0+2^2+4^2 = 20 & C D= 1^2+1^2+5^2 = 27 aligned ) and (D A= 0+2^2+4^2 = 20 ) Here, ( aligned & A B=C D and B C=D A & A C= 1^2+3^2+1^2 = 11 & and D B= 1^2+1^2+9^2 = 83 & A C D B aligned ) ( A, B, C ) and (D ) form a parallelogram.

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