Hello, magentarita!
Please check the wording of the problem.
As written, the facts are wrong.
Trapezoid TEAM has vertices: .$\displaystyle T(2,3),\;E(1,0),\;A(7,6),\;M(0,5)$
Points E, F(h,k) and A are on the same line.
If $\displaystyle T, E, F, M$ are the vertices of a square, find $\displaystyle h$ and $\displaystyle k.$ Code:

 o A
 * *
 * *
M * *
o *
*  . *
T o  . *
*  . *
* o F
 * *
    +  o          
 E

Quadrilateral $\displaystyle TEFM$ is not a square.
While $\displaystyle TM \perp TE$, the length of $\displaystyle TM$ is not equal to that of $\displaystyle TE.$
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
If this problem has multiple questions, okay.
. . Otherwise, it is stupidly written.
. . $\displaystyle \boxed{\begin{array}{c}\text{Three vertices of a rectangle are:}\\
M(0,5),\:T(\text{}2,3),\:E(1,0)\\
\text{Find }F\text{, the fourth vertex.}\end{array}}$
Who needs that trapezoid?