The question is about the formula for the coordinates of the  mid point of the line segment joining two points x1, y1 and x2,y2  .  The mid point is (x1+y1)/2 , (x2+y2)/2 .

 

For simplicity sake consider the points A,B,C and D all lying on X axis, with x-coordinates respectively 0, x1, x2 and x3.

 

The X-coordinate of the mid point M1of AB would be x1/2

             “                          “              M2 of CD would be (x2+x3)/2

 

The X-coordinate of M1M2 would thus be (x1+x2+x3)/2

 

The X-coordinate of the mid point  M3 of AD would be  x3/2

           “                             “              M4 of BC would be (x1+x2)/2

 

The mid point of M3M4 would thus be  ((x1+x2+x3)/2

 

This proves that the midpoint of M1M2 coincides with the mid point of M3M4 ..

 

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