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

1 Answer
Ananda Dasgupta
Jul 16, 2016

x+y-2 = 0x+y−2=0

Explanation:

Let (x,y)(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)(−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 (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(x+2)2−(x−6)2=(y−4)2−(y+4)2

Using a^2 -b^2 = (a+b)(a-b)a2−b2=(a+b)(a−b), this simplifies to

8(2x-4) = -8*2y8(2x−4)=−8⋅2y which simplifies to

x+y-2 = 0x+y−2=0

Related questions
See all questions in Perpendicular Bisectors
Impact of this question
12413 views around the world
You can reuse this answer
Creative Commons License