Question
Three vertices of a parallelogram ABCD are A(3,-1,2), B(1,2,4) and C(-1,1,2). Find the fourth vertex .
Answer: Option A
:
A
Let D(x,y,z) be the fourth vertex of the parallelogram.
The diagonals of a parallelogram bisect each other.
Therefore, the midpoints of AC and BD are the same. Let this be O.
O=(3−12,−1+12,2+22)O=(1,0,2)
Now, O is the midpoint of BD
∴1+x2=1⇒x=12+y2=0⇒y=−24+z2=2⇒z=0
D=(1,0,2)
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:
A
Let D(x,y,z) be the fourth vertex of the parallelogram.
The diagonals of a parallelogram bisect each other.
Therefore, the midpoints of AC and BD are the same. Let this be O.
O=(3−12,−1+12,2+22)O=(1,0,2)
Now, O is the midpoint of BD
∴1+x2=1⇒x=12+y2=0⇒y=−24+z2=2⇒z=0
D=(1,0,2)
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