SOLUTION: the points A(3,2) and B(2,-3) are equidistant from a point P(x,y). find the relation beween x and y.

Algebra ->  Length-and-distance -> SOLUTION: the points A(3,2) and B(2,-3) are equidistant from a point P(x,y). find the relation beween x and y.      Log On


   

Question 942849: the points A(3,2) and B(2,-3) are equidistant from a point P(x,y). find the relation beween x and y.
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Perpendicular Bisector of AB.

Slope for AB is %282-%28-3%29%29%2F%283-2%29=5. The line perpendicular to AB must have slope -1%2F5.

Midpoint of AB is
x=%283%2B2%29%2F2=5%2F2
and
y=%282%2B%28-3%29%29%2F2=-1%2F2.
As ordered pair of coordinates, this midpoint is (5/2,-1/2).

The line for any point P will be highlight_green%28y-%28-1%2F2%29=%28-1%2F5%29%28x-5%2F2%29%29 using POINT-SLOPE form for equation of a line. Simplify and put into whatever form you want.