Question 112503
Start by labeling the intersection of the two lines FG and PQ with an O.


Since PQ is a perpendicular bisector of FG, we know that segments FO and OG must be equal.  And since PO = PO and angle FOP = angle GOP because FG and PQ are perpendicular, we know that {{{DELTA*FOP}}} is congruent to {{{DELTA*GOP}}}.  Now we can say for certain that FP = PG, therefore,


{{{4x-9=2x/3+21}}}
{{{4x-2x/3=30}}}
{{{12x/3-2x/3=30}}}
{{{10x/3=30}}}
{{{10x=90}}}
{{{x=9}}}


Similarly, we can show that FQ = QG, hence,


{{{9y/2-4=5y-6}}}
{{{9y/2-5y=-6+4}}}
{{{9y-10y=-12+8}}}
{{{-y=-4}}}
{{{y=4}}}


And there you have it.


Hope that helps,
John