AP EAMCET Engineering 2018 Apr 24 Shift 1 Paper

The coordinates of the mid-points are D(1,5,−1),E(0,4,−2),F(2,3,4) The relation between the coordinates of vertex of triangle and the mid points is

x1+x2

2

=1,

y1+y2

2

=5,

z1+z2

2

=−1
x1+x2=2,y1+y2=10,z1+z2=−2
For other two sides,
x2+x3=0,y2+y3=8,z2+z3=−4
x1+x3=4,y1+y3=6,z1+z3=8
By using the above relations
2(x1+x2+x3)=6
2(y1+y2+y3)=24
2(z1+z2+z3)=2
x3=1,y3=2,z3=3
The length of the median CD is
CD=√(1−1)2+(2−5)2+(−1−3)2 =5