Triangle ABC has coordinates A(3, -2), B(8, 2), and C(5, 10).

To find a revolution of 270^o, I would do this:  the y-value of the initial point becomes the x-value after rotation

                                                                       the negative of the initial x-value becomes teh y-value after rotation.

A(3, -2)   --->   A'(-2, -3)

B(8, 2)   --->   B'(2, -8)

C(5, 10)   --->   C'(10, -5)

 

But, graph these to check to see if this works!

 

I'm assuming that the notation "T_1,-6" means a translation of 1 of the x-value and -6 of the y-value:

A(3, -2)   --->   A''(4, -8)

B(8, 2)   --->   B''(9, -4)

C(5, 10)   --->   C''(6, 4)

 

To see whether they are congruent or not, graph them and measure. My initial response is that they will be congruent because rotations and translation preserve distance and angles.