Given :
[tex]C(\dfrac{5}{3},-6)\ , \ B(\dfrac{8}{3},4)[/tex] .
B is the mid-point of AC .
To Find :
The missing endpoint if B is the midpoint of AC.
Solution :
Let , coordinate of point A is ( h, k) .
So , mid-point B is given by :
[tex](\dfrac{\dfrac{5}{3}+h}{2},\dfrac{-6+k}{2})[/tex]
Comparing above point with [tex]B(\dfrac{8}{3},4)[/tex] , we get :
[tex]\dfrac{\dfrac{5}{3}+h}{2}=\dfrac{8}{3}\\\\h+\dfrac{5}{3}=\dfrac{16}{3}\\\\h=\dfrac{11}{3}[/tex] [tex]\dfrac{-6+k}{2}=4\\\\k=14[/tex]
Therefore , the value of point A is [tex](\dfrac{11}{3},14)[/tex] .
Hence , this is the required solution .
