For this line PS to be the hypotenuse of an isosceles
right triangle,
 

 
We could have two possibilities for such an
isosceles right triangle. This is one 
possibility for T, call it little "t".
 

 
This is another possibility for T, we'll
call it big T.
 

 
Put them together side by side and you have
a square:
 

 
Now from P to S is 7 units. That means that the diagonal of 
the square is 7 units long.  We also know that both diagonals
have the same length, so let's draw in the other diagonal Tt,
from the T on the left to the t on the right, crossing the other
diagonal PS at their common midpoint X: 

 

Tt has to also be 7 units long. because PS is.
That makes Xt be half of that or 3.5 units long.
Now X is 6 units horizontally away from the y-axis
and since Xt = 3.5 units, t has to be 6-3.5 or 2.5
units from the y-axis.  That means the x-coordinate 
of t has to be -2.5.  

We know what the y-coordinate of t is because it's 
the same as the y-coordinate of X.  That's the 
midpoint of P(-6,-2) and P(-6,5), or X(-6,1.5), and 
so t is the point t(-2.5,1.5).

Use the same reasoning and you'll get that the 
coordinates of T are T(-9.5,1.5)

Edwin