A few days ago

whaddyaknow?

Help with a proof? about perpendicular bisectors?

Prove that any point equidistant from the two endpoints on a line segment lies on the perpendicular bisector or that segment.

I already proved that any point on the perpendicular bisector is equidistant from the two endpoints of the line segment, but I’m stuck on this one.

Thanks a ton! 🙂

Top 3 Answers

A few days ago

Jamres

Favorite Answer

EDIT:

let L = Length of linesegment

let u = location along the line segment from which a perpendicular line is constructed

let h = perpendicular height from the line to the point that will be considered.

If point p is on the perpendicular bisector then: u = 1/2 L

—

now we know p is equidistant to both ends, using pythagorus:

u^2 + h^2 = (L-u)^ 2 + h^2 [Known]

u^2 = L^2 – 2uL – u^2

0 = L^2 -2uL

2u = L

u = 1/2 L , but this meant that the point was on a perpendicular bisector.

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Well, at least you understand it. I don’t. 😉

4 years ago

Draw a Line connecting EA (There can in ordinary terms be one line) Draw a Line connecting EB (There can in ordinary terms be one line) advert = DB (definition of perpendicular bisector) < ADE =

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Help with a proof? about perpendicular bisectors?

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