Question

If M is the midpoint of segment AB, find the coodinates of B; given that A = (-8,9) and M= (-6,6).  Calulate the distance between A and B

Find the equation in point-slope form of the line that is the perpendicular bisector of the segment between (16,-4) and (-2,-76).

Answer 1

Midpoint of a line is the average of the coords of the end points. If B is (x,y) then (x-8)/2=-6 and (y+9)/2=6, and x=-12+8=-4 and y=12-9=3. B is (-4,3).

The midpoint of (16,-4) and (-2,-76) is (7,-40), being the average of the endpoint coords. The slope of the segment is (-76+4)/(-2-16)=-72/(-18)=4 so the slope of the perpendicular is -4 and the point-slope form of the equation of the perpendicular is (y+40)=-4(x-7) or (y+40)=4(7-x), where the reference point is the midpoint (7,-40) of the line segment.