Problem:
Let points A=(0,0,0),B=(1,0,0),C=(0,2,0), and D=(0,0,3). Points E, F,G, and H are midpoints of line segments BD,AB,AC, and DC respectively. What is the area of EFGH?
Answer Choices:
A. 2​
B. 325​​
C. 435​​
D. 3​
E. 327​​
Solution:
The midpoint formula gives E=(21​,0,23​),F=(21​,0,0),G=(0,1,0), and H=(0,1,23​). Note that EF=GH=23​,EF⊥EH,GF⊥GH, and
EH=FG=(21​)2+12​=25​​.
Therefore EFGH is a rectangle with area 23​⋅25​​=(C)435​​​.
