I've gotten to the point where I have the following equation: 2 x 2 x m − 2 x m x 1 + 2 y 2 y m − 2 y m y 1 = x 2 2 − x 1 2 + y 2 2 − y 1 2 Would it be mathematically correct to split this into the following two equations { 2 x 2 x m − 2 x m x 1 = x 2 2 − x 1 2 2 y 2 y 2 − 2 y m y 1 = y 2 2 − y 1 2 and treat them as a system of equations? If so, then how would I go about doing this?

Question

I&#039;ve gotten to the point where I have the following equation:  2      x    2        x    m    −  2      x    m        x    1    +  2      y    2        y    m    −  2      y    m        y    1    =      x    2    2    −      x    1    2    +      y    2    2    −      y    1    2  Would it be mathematically correct to split this into the following two equations      {                            2                      x            2                                x            m                    −          2                      x            m                                x            1                    =                      x            2            2                    −                      x            1            2                                                2                      y            2                                y            2                    −          2                      y            m                                y            1                    =                      y            2            2                    −                      y            1            2                                  and treat them as a system of equations? If so, then how would I go about doing this?

Mateo Carson · Accepted Answer

Step 1You can not split this equation. That would be the same as saying   a  +  b  =  c  +  d can be split into   a  =  c and   b  =  d .If the points are       P    1    ,      P    2    , and       P    m   , for       P    m   to be the midpoint between       P    1   and       P    2   , then one way of writing this is that       P    m   must be on the line between       P    1   and       P    2   (i.e.,       P    m    =  t      P    1    +  (  1  −  t  )      P    2   for   0  ≤  t  ≤  1 ) and       P    m   must be at the halfway position (i.e.,   t  =      1    2   ).Another way is that       |        P    1    −      P    m        |    =      |        P    2    −      P    m        |   and       |        P    1    −      P    m        |    =      |        P    2    −      P    1        |        /    2 . This way gives you two equations for the two unknowns of the x and y components of       P    m   .