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)M=(x1+x22,y1+y22)
Where MM is the midpoint and the given points are:
(color(red)(x_1), color(red)(y_1))(x1,y1) and (color(blue)(x_2), color(blue)(y_2))(x2,y2)
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=(25+132,−15+522)
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=⎛⎜⎝(33×25)+(55×13)2,(22×−15)+(55×52)2⎞⎟⎠
M = ((6/15 + 5/15)/2 , (-2/10 + 25/10)/2)M=(615+5152,−210+25102)
M = ((11/15)/2 , (-23/10)/2)M=(11152,−23102)
M = (11/(15 xx 2) , -23/(10 xx 2))M=(1115×2,−2310×2)
M = (11/30 , -23/20)M=(1130,−2320)
