If G is the midpoint of FH, find FG

Answer 1

If the co-ordinates of F are (a,c) and the co-ordinates of H are (b,d),

the co-ordinates of G are [(a+b)/2,(c+d)/2)].

Answer 2

Juan asks “…find FG,” which is a distance, which implies using the distance formula…

       d = √ [(x₂-x₁)²+(y₂-y₁)²]

Extending the information from Paul’s accurate response from above, let’s substitute his coordinate assignments for points F (point #1) and midpoint G (point #2) into the distance formula to get…

       FG = √ [(((a+b)/2)-a)²+(((c+d)/2)+c)²]

…which expands and simplifies to…

       FG = ½√ [(a²-2ab+b²) + (c²-2cd+d²)]

To check, let’s test by graphing, say, points F(1,6)—>(a,b), 

H(13,1)—>(c,d).  The graph of the midpoint is read G(7,3.5) which is in agreement with Paul’s calculation.  Substitute numerical values for a thru d in the above formula yields FG=6.5units.  Test other easily graphed lines to verify.  Always check your work.