SOLUTION: the distance of point P(6,p) from the y-axis is equal to its distance from a point Q(6,3).find the length of PQ and the possible values of P

Algebra ->  Linear-equations -> SOLUTION: the distance of point P(6,p) from the y-axis is equal to its distance from a point Q(6,3).find the length of PQ and the possible values of P      Log On


   

Question 887082: the distance of point P(6,p) from the y-axis is equal to its distance from a point Q(6,3).find the length of PQ and the possible values of P
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the distance formula,
D%5E2=%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2
.
.
.
Distance from P to x-axis:
D%5B1%5D%5E2=%286-x%29%5E2%2B%28p-0%29%5E2=%286-x%29%5E2%2Bp%5E2
Distance from P to Q:
D%5B2%5D%5E2=%286-6%29%5E2%2B%28p-3%29%5E2=%28p-3%29%5E2
Set the two distances equal to each other,
%286-x%29%5E2%2Bp%5E2=%28p-3%29%5E2
%286-x%29%5E2%2Bp%5E2=p%5E2-6p%2B9
-6p%2B9=%286-x%29%5E2
-6p=%286-x%29%5E2-9
highlight%28p=-%281%2F6%29%286-x%29%5E2%2B3%2F2%29