Show that the points A(3,3,3) B(0,6,3) C(1,7,7) and D(4,4,7) are the vertices of a square - Maths - Introduction to Three Dimensional Geometry

Question

Show that the points A(3,3,3) B(0,6,3) C(1,7,7) and D(4,4,7) are
the vertices of a square

Rishabh Mittal · Accepted Answer

Dear Student ,

Please find below the solution to the asked query :

Distance=x2-x12+y2-y12+z2-z12Now,AB=0-32+6-32+3-32=9+9+0=18=32 unitsBC=1-02+7-62+7-32=1+1+16=18=32 unitsCD=4-12+4-72+7-72=9+9+0=18=32 unitsDA=3-42+3-42+3-72=1+1+16=18=32 unitsAB=BC=CD=DA⇒ All four sides are equalNow,AC=1-32+7-32+7-32=4+16+16=36=6 unitsBD=4-02+4-62+7-32=16+4+16=36=6 unitsAC=BD⇒Diagonals are also equal
So,it is a square
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