# Set of points equidistant from two points

• lat3ralus65
In summary, the task is to find an equation for the set of points equidistant from A(-1,5,3) and B(6,2,-2). The set can be described as a plane between the two points. The equation for a plane can be used to solve this problem.
lat3ralus65

## Homework Statement

Find an equation of the set of all points equidistant from the points A(-1,5,3) and B(6,2,-2). Describe the set.

None...

## The Attempt at a Solution

Um, I've drawn a graph of the two points and that's about as far as I could get. I know the answer should be a plane going between the two points... but how do I find the equation?

lat3ralus65 said:
Um, I've drawn a graph of the two points and that's about as far as I could get. I know the answer should be a plane going between the two points... but how do I find the equation?

Do you know how to write a generic equation for a plane?

## 1. What does it mean for a set of points to be equidistant from two points?

Equidistant means that the points are all the same distance away from two given points. In other words, the points are equally distant from both given points.

## 2. How do you find the set of points equidistant from two points?

To find the set of points equidistant from two points, you can use the midpoint formula. This formula calculates the point that is exactly halfway between the two given points. Then, you can use this point as the center and draw a circle with a radius equal to the distance between the two given points. The points on this circle will be equidistant from the two given points.

## 3. Can there be more than one set of points equidistant from two points?

Yes, there can be multiple sets of points that are equidistant from two points. This is because any point on the circle drawn with the midpoint as the center and the distance between the two given points as the radius will be equidistant from the two given points.

## 4. What is the significance of a set of points equidistant from two points?

A set of points equidistant from two points is significant in geometry and can be used in various calculations and constructions. For example, in triangle constructions, the perpendicular bisector of a side will pass through the set of points equidistant from the two endpoints of that side.

## 5. How is the set of points equidistant from two points related to the concept of symmetry?

The set of points equidistant from two points is an example of reflection symmetry. This is because every point on this set has a mirror image on the other side of the line passing through the two given points. This line of symmetry divides the set into two equal halves, making it symmetrical.

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