I think your question in correct way is like this:
ST lines on the coordinate plane with S located at (3,2). The midpoint of ST is Z(3,9). Can the location of T be determined? If so, state the location. If not, explain why not.
Answer:
T(3,16)
Step-by-step explanation:
If two points A([tex]x_{a}[/tex],[tex]y_{a}[/tex]) and B([tex]x_{b}[/tex],[tex]y_{b}[/tex]) are given then the coordinate of midpoint of AB is given by M([tex]\frac{x_{a}+x_{b}}{2}[/tex],[tex]\frac{y_{a}+y_{b}}{2}[/tex]).
Similarly coordinates of Z in terms of coordinates of S and T is given by:
[tex]x_{z}=\frac{x_{s}+x_{t}}{2}\\3=\frac{3+x_{t}}{2}\\6=3+x_{t}\\ \therefore x_{t}=3[/tex]
[tex]y_{z}=\frac{y_{s}+y_{t}}{2}\\9=\frac{2+y_{t}}{2}\\18=2+y_{t}\\ \therefore y_{t}=16[/tex]
Therefore, point T is located at (3,16).
