document.write( "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?
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Algebra.Com's Answer #843669 by mananth(16946) $\"\"$ $\"About$

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Let the intersection at X axis be (0,y)\r
\n" ); document.write( "\n" ); document.write( "PA =PB Any point on the perpendicular bisector is equidistant from the endpoints\r
\n" ); document.write( "\n" ); document.write( "Distance formula\r
\n" ); document.write( "\n" ); document.write( " $\"d=+sqrt%28%28x1-x2%29%5E2%2B%28y1-y2%29%5E2%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "PA^2= PB^2\r
\n" ); document.write( "\n" ); document.write( "((1-0)^2+(2-y)^2)= (3-0)^2+(4-y)^2\r
\n" ); document.write( "\n" ); document.write( "1+4-4y+y^2=9+16-8y+y^2\r
\n" ); document.write( "\n" ); document.write( "rearrange\r
\n" ); document.write( "\n" ); document.write( "8y-4y = 25-5\r
\n" ); document.write( "\n" ); document.write( "4y = 20
\n" ); document.write( "y= 5\r
\n" ); document.write( "\n" ); document.write( "PA^2 =((1-0)^2+(2-5)^2)=10
\n" ); document.write( "PA= sqrt(10)\r
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