SOLUTION: My problem does not come from a textbook my teacher gave it to me in a packet...the information that was given is that line PQ is the perpendicular bisector of line segment FG.Lin

Algebra ->  Triangles -> SOLUTION: My problem does not come from a textbook my teacher gave it to me in a packet...the information that was given is that line PQ is the perpendicular bisector of line segment FG.Lin      Log On


   

Question 112503: My problem does not come from a textbook my teacher gave it to me in a packet...the information that was given is that line PQ is the perpendicular bisector of line segment FG.Line FP=4X-9,PG=2/3x+21,FQ=9/2y-4 and QG=5y-6 what is the value of x and y?
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
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%2AFOP is congruent to DELTA%2AGOP. Now we can say for certain that FP = PG, therefore,

4x-9=2x%2F3%2B21
4x-2x%2F3=30
12x%2F3-2x%2F3=30
10x%2F3=30
10x=90
x=9

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

9y%2F2-4=5y-6
9y%2F2-5y=-6%2B4
9y-10y=-12%2B8
-y=-4
y=4

And there you have it.

Hope that helps,
John