SOLUTION: Find the equation of the perpendicular bisector of the segment AB, if A(1, 2) and B(�3, 4). If the perpendicular bisector of AB intercepts the x-axis at point P, what are the len

Algebra ->  Length-and-distance -> SOLUTION: Find the equation of the perpendicular bisector of the segment AB, if A(1, 2) and B(�3, 4). If the perpendicular bisector of AB intercepts the x-axis at point P, what are the len      Log On


   

Question 1124692: Find the equation of the perpendicular bisector of the segment AB, if A(1, 2) and B(�3, 4). If the perpendicular bisector of AB intercepts the x-axis at point P, what are the lengths of PA and PB?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Let the intersection at X axis be (0,y)
PA =PB Any point on the perpendicular bisector is equidistant from the endpoints
Distance formula
d=+sqrt%28%28x1-x2%29%5E2%2B%28y1-y2%29%5E2%29

PA^2= PB^2
((1-0)^2+(2-y)^2)= (3-0)^2+(4-y)^2
1+4-4y+y^2=9+16-8y+y^2
rearrange
8y-4y = 25-5
4y = 20
y= 5
PA^2 =((1-0)^2+(2-5)^2)=10
PA= sqrt(10)
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