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# Answer to Question #5854 in Abstract Algebra for nayeli correa

Question #5854
Write an equation of the perpendicular bisector of the line segment whose endpoints are (-1,1) and (7,-5)
1) Let’s call the one endpoint (-1,1) as point A and another endpoint (7,-5) as point B
2) Let’s find the middle point of the line segment AB – the point, called C
We can use it to make the perpendicular bisector.
3) Let’s find the equation of the line , on which there are points A and B. Lets called this line L
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The normal vector of this line L is (3,4). It also would be a directional vector of the perpendicular line K to the line L
4) Let’s find the equation of the line K using that C is lay on the line K
But :
If you want the equation of the perpendicular line without using the point C(the general look of the equation), it would be
4x-3y+z=0 ,
where z is any integer.

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