Question 1209346
<font color=black size=3>
Answer: <font color=red>(5,13)</font>


Explanation:


To go from B to C we go up 9 and right 2
Start at point A(3,4) and go up 9 and right 2 so you arrive at <font color=red>(5,13)</font> 
This is where D should be placed to get parallelogram ABCD.


Technically there are 2 other spots D could go if we didn't care about the order of ABCD. But I'll assume that the order matters.


To prove that ABCD is a parallelogram, you need to show that
slopeAB = slopeCD
slopeBC = slopeAD
I'll let the student do these verifications. The slope formula is 
m = (y2-y1)/(x2-x1)
or you can use the rise/run concept. 


{{{
drawing(400,400,-3,8,-2,15,
graph(400,400,-3,8,-2,15),
circle(3,4,0.08),circle(3,4,0.095),circle(4,-1,0.08),circle(4,-1,0.095),circle(6,8,0.08),circle(6,8,0.095),circle(5,13,0.08),circle(5,13,0.095),
line(3,4,4,-1),line(4,-1,6,8),line(6,8,5,13),line(5,13,3,4),

line(3.9411764706,8.2352941176,4.06,7.72),line(3.9411764706,8.2352941176,3.62,7.9),line(4.0602352941,8.7710588235,3.76,8.4),line(4.0602352941,8.7710588235,4.2,8.26),line(4.9896470588,3.4534117647,4.68,3.16),line(4.9896470588,3.4534117647,5.16,2.98),line(5.1016470588,3.9574117647,4.78,3.64),line(5.1016470588,3.9574117647,5.28,3.44),line(3.4715384615,1.6423076923,3.56,2.48),line(3.4715384615,1.6423076923,3.08,2.12),line(5.6515384615,9.7423076923,5.26,10.1),line(5.6515384615,9.7423076923,5.84,10.34),

locate(3-0.5,4,"A"),
locate(4,-1-0.2,"B"),
locate(6+0.2,8,"C"),
locate(5+0.2,13,"D=(5,13)")
)
}}}
</font>