Find an equation describing all points P(x,y) equidistant from ( -2,4) and (5,-1). Write your answer in general form.

Question

Thank you.

Answer 1

The midpoint is ((5-2)/2,(4-1)/2)=(3/2,3/2). The slope of the line joining the points is (4-(-1))/(-2-5)=-5/7. So the slope of the perpendicular bisector is 7/5. The equation of the perpendicular is y-3/2=7(x-3/2)/5.

This works out as y=7x/5-21/10+1.5 or y=1.4x-0.6.