what values of a and b make quadrilateral MNOP a parallelogram?no=21 op=13 mp=4a+b mn=3a-2b
If the quadrilateral is a parallelogram then
$\displaystyle |\overline{MN}| = |\overline{OP}| = 13$
and
$\displaystyle |\overline{PM}| = |\overline{ON}| = 21$
That means you have a system of simultaneous equations:
$\displaystyle \left|\begin{array}{lcr}4a+b&=&21\\3a-2b&=&13\end{array}\right.$
I've got a = 5 and b = 1