MHT CET 2020 Math Solved Paper

Let D(x,y,z) be the required point, Then, the mid-point of diagonal BD is
(‌

x+1

2

,‌

y+2

2

,‌

z−4

2

)
Also, the mid-point of diagonal AC is
(‌

3−1

2

,‌

−1+1

2

,‌

2+2

2

) i.e., (1,0,2)
But, the mid-points of the diagonals of a parallelogram always coincide.
∴‌

x+1

2

=1,‌

y+2

2

=0 and ‌

z−4

2

=2
So, x=1,y=−2, and z=8.
Hence, the required point is D(1,−2,8).