Three vertices of a Paralellagram Three vertices of a parallelogram have 
coordinates (0,1), (3,7), and (4,4).  
Name a point that could represent the fourth vertex of the parallelogram..
 A: There are several points that could be used to complete the parallelogram. To find one of those points, take two of the given vertices (say (0,1) and (3,7)) and find the difference between those points (in this case (3,6)).  Then add or subtract that difference to the third vertex (4,4) to get the fourth point.
A: You have three possible choices, depending on what is the common vertex of two adjacent sides of the parallelogram.
Let $A=(0,1)\quad B=(3,7) \quad C=(4,4)$
If you choice as sides $AB$ and $AC$ that this sides are parallel to the vectors $\vec{AB}=(x_B-x_A,y_B-y_A)=(3,6)$ and $\vec{AC}=(x_C-x_A,y_C-y_A)=(4,3)$.
In this case the vertex $D_1$ of the parallelogram can be found adding one of these vectors to one of the two vertex $B$ and $C$ (this is the famous parallelogram low), so we find:
$$
D_1=B+\vec{AC}=C+\vec{AB}
$$
And you can test that the two additions gives the same result $D_1=(7,10)$
In the same way you can use $\vec{CB}=(-1,3)$ and $\vec{CA}=(-4,-3)$ and find:
$$
D_2=A+\vec{CB}=B+\vec{CA}
$$
or $\vec{BA}=(-3,-6)$ and $\vec{BC}=(1,-3)$ and find:
$$
D_3=A+\vec{BC}=C+\vec{BA}
$$
