the answer:
the main rule of transformation are as follow
Reflection:a reflection in the line y = x changes the point (x; y) to (y; x)
the transformation T(a, b), changes changes the point (x; y) to (x+a ; y+ b)
the construction of the image is as follow:
as for T(3, 7), the image is T"(8, 1)
so with the reflection in the line y = x, T(3, 7) becomes T' (7, 3), and with the transformation T(1, –2), the point T' (7, 3) becomes (7+1, 3 -2) =T"(8, 1)
with the reflection in the line y = x, U(6, –6) becomes U'(-6, 6), and with the transformation T(1, –2), the point U'(-6, 6) becomes (-6 +1, 6-2)=U"(–5, 4)
with the reflection in the line y = x, V(5, –9) becomes V'(-9, 5), and with the transformation T(1, –2), the point V'(-9, 5) becomes (-9 +1, 5-2)=U"(–8, 3)
so the final answer is
r y = x and then T(1, –2)
