I kept wondering of the best way to "see" why midpoint of A = x 1 , B = x 2 is ( x 1 + x 2 ) / 2.

Question

I kept wondering of the best way to &quot;see&quot; why midpoint of   A  =      x    1    ,  B  =      x    2   is   (      x    1    +      x    2    )      /    2.

Melina Glover · Accepted Answer

Step 1Here&#039;s one way to visualize it with the help of some algebra: Suppose       x          1        &amp;lt;      x          2       . Then the midpoint means finding a point xm such that       x          m        =      x          1        +  a and       x          m        =      x          2        −  a as in the image below.This means that      x          1        +  a  =      x          2        −  a    ⟹    a  =                    x                  2                    −              x                  1                      2  and so      x          m        =      x          1        +  a  =      x          1        +                    x                  2                    −              x                  1                      2    =                    x                  1                    +              x                  2                      2    .

Isabela Sherman · Accepted Answer

Step 1If we are on the real line we have that the mid point of       x    1    &amp;lt;      x    2   is the point x such that:  x  −      x    1    =      x    2    −  x    ⟺    2  x  =      x    1    +      x    2  which is exactly what we want.

I kept wondering of the best way to "see" why midpoint of A = x 1 </msub>

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