If we take the difference in the x and y values for corresponding points (x,y) for triangles TUV and T"U"V" we can see that they are congruent. Call these differences x(TU)=3-6=-3; y(TU)=7+6=13; x(TV)=-2; y(TV)=16; x(UV)=1; y(UV)=3. For the other triangle: y(U"T")=3; x(T"U")=13; y(T"V")=-2; x(T"V")=16; y(U"V")=1; x(U"V")=3.
So the transformation requires swapping of the axes (rotation and reflection) and displacement:
T(3,7)⇒(7,3); U(6,-6)⇒(-6,6); V(5,-9)⇒(-9,5) (rotation and reflection)
(7,3)⇒T"(7+1,3-2); (-6,6)⇒U"(-6+1,6-2); (-9,5)⇒V"(-9+1,5-2) (displacement)