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:
#M = ((color(red)(2/5) + color(blue)(1/3))/2 , (color(red)(-1/5) + color(blue)(5/2))/2)#
#M = (((3/3 xx color(red)(2/5)) + (5/5 xx color(blue)(1/3)))/2 , ((2/2 xx color(red)(-1/5)) + (5/5 xx color(blue)(5/2)))/2)#
#M = ((6/15 + 5/15)/2 , (-2/10 + 25/10)/2)#
#M = ((11/15)/2 , (-23/10)/2)#
#M = (11/(15 xx 2) , -23/(10 xx 2))#
#M = (11/30 , -23/20)#
