Math Is Fun Forum

mathland

Member

Registered: 2021-03-25

Posts: 444

Equidistance

Find a relationship between x and y
such that (x, y) is equidistant (the same distance)
from the two points.

Given two points: A(6, 5), B(1, −8)

Is this question asking for the midpoint of AB?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Equidistance

That's the correct place to start.

But we need all the points that are equidistant.  So you need the perpendicular bisector of AB

https://www.mathsisfun.com/geometry/con … isect.html

Steps: 1.  work out the gradient of AB

2. Hence the gradient of a line that is perpendicular to AB.

3. Using that and the midpoint, work out the equation of that line.

B.

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathland

Member

Registered: 2021-03-25

Posts: 444

Re: Equidistance

That's the correct place to start.

But we need all the points that are equidistant.  So you need the perpendicular bisector of AB

https://www.mathsisfun.com/geometry/con … isect.html

Steps: 1.  work out the gradient of AB

2. Hence the gradient of a line that is perpendicular to AB.

3. Using that and the midpoint, work out the equation of that line.

B.

Good steps and should be easy to do.