Find the coordinates of the other endpoint of the segment gi

Find the coordinates of the other endpoint of the segment given its midpoint M and one endpoint Q. M(b, m), Q(g, r) The second endpoint is P

Solution

midpoint = ( b,m )

one end point = ( g , r )

midpoint is given by the formula

M = x1 + x2 / 2   , y1 + y2 / 2

b = g + x2 / 2   , m = r + y2 / 2

x2 = ( 2b - g )   , y2 = ( 2m - r )

hence, other endpoint is

( 2b - g ) , ( 2m - r )