How do I find the equation of a perpendicular bisector of a line segment with the endpoints (−2,−4) and (6,4)?

1 Answer
Ananda Dasgupta
Jul 16, 2016

x+y−2=0

Explanation:

Let (x,y) be any point on the perpendicular bisector. From elementary geometry, we can easily see that this point must be equidistant from the two points (−2,−4)and(6,4). Using the Euclidean distance formula gives us the equation

(x+2)2+(y+4)2=(x−6)2+(y−4)2

This can be rewritten as

(x+2)2−(x−6)2=(y−4)2−(y+4)2

Using a2−b2=(a+b)(a−b), this simplifies to

8(2x−4)=−8⋅2y which simplifies to

x+y−2=0

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