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Question 1133923: Find the equation of the perpendicular bisector of the segment AB, if A(3, 0) and B( - 1, 2). If the perpendicular bisector of AB intercepts the x-axis at point P, what are the lengths of PA and PB?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! the midpoint is the middle of the x values and of the y values, which is (1, 1)
The perpendicular bisector has slope which is the negative reciprocal of the slope of AB, and the latter slope is (2/-4) or -(1/2).
Point slope formula y-y1=m(x-x1), m slope and (x1, y1) a point. For the equation of AB, it is y-0=(-1/2)(x-3) or y=(-1/2)x+(3/2)
For the perpendicular line, the slope is 2 and the point slope equation is y-1=2(x-1) or y=2x-1. That reaches the x-axis at y=0 so 2x-1=0 and x=0.5, so the point is (0.5, 0)
reaches x-axis where y=0 or 2x=6 and x=3, so (3, 0) is point
Distance to A (PA) is sqrt (difference in x^2+difference in y^2) or sqrt (1.5^2+2^2)=sqrt(6.25) or 2.5 units. Of course, the distance between (0.5, 0) and (3, 0) is 2.5 units ANSWER
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