Points equidistant from 2 given points: Find the relationship between x and y so that the point (x,y) is equidistant from (3, 2) and (-3, -4).

We can use the general point (x, y) in the Distance Formula to express its distance from each point, and then require that the distances be equal. For convenience, we can use the square of the distance.

For the points (x, y) and (-3, -4):

For the points (x, y) and (3, 2):

Equating these two quantities, we get

, or

, or

Hence the desired points are located on the line given by the last result.