Question

If $A,B.C$ are $(3,3,3),(0,6,3)$ and $(1,7,7)$ respectively. find $D(x,y,z)$ such that ABCD is a square

Answer 1

$LetmidpointofdiagonalsbeM.thenco-ordinateofMwillbeauniquevalueusingAandC,co-ordinatesofmid-pointsofdiagonalsare\left(\right(\frac{3+1}{2}),(\frac{3+7}{2}),(\frac{3+7}{2}\left)\right)=M(2,5,5)nowusingBandD,co-ordinatesofmid-pointsshouldbeM\left(\right(\frac{x+0}{2}),(\frac{y+6}{2}),(\frac{z+3}{2}\left)\right)bycomparing,weget\left(\frac{x}{2}\right)=2orx=4\left(\frac{y+6}{2}\right)=5ory=10-6=4\left(\frac{z+3}{2}\right)=5orz=10-3=7\therefore M(4,4,7)$