Atriangle has vertices t(3, 7), u(6, –6), and v(5, –9). the image of the triangle has vertices t"(8, 1), u"(–5, 4), and v"(–8, 3).

which transformations could have produced the image?

t(1, –2) ry = x
ry = x t(1, –2)

The

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)