Question 1046069
They can be.  What you looking for?  The line which perpendicularly bisects the segment contains points which will form isosceles triangle with your given points.  


Find slope for points  (6,7) and (-8,-1).
Find negative reciprocal of this slope.
Find midpoint of the two points.
Plug into the point-slope equation form of a line.
That is the line which contains the points you want.  You can pick any point you want on this line as long as the picked point is  NOT the found midpoint.