The formula to find the mid-point of a line segment give the two end points is:

#M = ((color(red)(x_1) + color(blue)(x_2))/2 , (color(red)(y_1) + color(blue)(y_2))/2)#

Where #M# is the midpoint and the given points are:

#(color(red)(x_1), color(red)(y_1))# and #(color(blue)(x_2), color(blue)(y_2))#

Substituting the values from the points in the problem gives:

#(1, 4) = ((color(red)(5) + color(blue)(x_2))/2 , (color(red)(1) + color(blue)(y_2))/2)#

We can now solve for #color(blue)(x_2)# and #color(blue)(y_2)#

#(color(red)(5) + color(blue)(x_2))/2 = 1#

#color(green)(2) xx (color(red)(5) + color(blue)(x_2))/2 = color(green)(2) xx 1#

#cancel(color(green)(2)) xx (color(red)(5) + color(blue)(x_2))/color(green)(cancel(color(black)(2))) = 2#

#color(red)(5) + color(blue)(x_2) = 2#

#color(red)(5) - color(green)(5) + color(blue)(x_2) = 2 - color(green)(5)#

#0 + color(blue)(x_2) = -3#

#color(blue)(x_2) = -3#

#(color(red)(1) + color(blue)(y_2))/2 = 4#

#color(green)(2) xx (color(red)(1) + color(blue)(y_2))/2 = color(green)(2) xx 4#

#cancel(color(green)(2)) xx (color(red)(1) + color(blue)(y_2))/color(green)(cancel(color(black)(2))) = 8#

#color(red)(1) + color(blue)(y_2) = 8#

#color(red)(1) - color(green)(1) + color(blue)(y_2) = 8 - color(green)(1)#

#0 + color(blue)(y_2) = 7#

#color(blue)(y_2) = 7#

**The Other End Point Is:** #(color(blue)(-3), color(blue)(7))#