Given two points A(2, -3) and B(5, 8).Can you find a point C(x,y) that is equidistant from A and B? d(A,C) = d(B,C)d represents a distance?



The midpoint c( (2 + 5)/2 , (-3 + 8)/2) ) c(3.5, 2.5) <––––––  

Spock (rhp)

the first such point, rather obviously, is ( {[2 + n5]/2}, {[-3 + 8]/2} ) [the simple average of the x and y coordinates is the point exactly midway between the two given points and located exactly on the line the two points form.] It is a bit trickier to show that all possible points that are equidistant between A and B lie on the perpendicular to the line the two points form that is exactly half way along [ie: at the point I described earlier.]