Answer:
Yes
Step-by-step explanation:
Under a counterclockwise rotation about the origin of 270°
a point (x, y ) → (y, - x )
Thus
A(1, 1 ) → A'(1, - 1 )
B(1, 4 ) → B'(4, - 1 )
C(3, 4 ) → C'(4, - 3 )
D(6, 1 ) → D'(1, - 6 )
These are the correct coordinates for the diagram A'B'C'D'
A translation (x, y ) → (x + 4, y + 1 )
Add 4 to the x- coordinates and add 1 to the y- coordinates, that is
A'(1, - 1 ) → A''(1 + 4, - 1 + 1 ) → A''(5, 0 )
B'(4, - 1 ) → B''(4 + 4, - 1 + 1 ) → B''(8, 0 )
C'(4, - 3 ) → C''(4 + 4, - 3 + 1 ) → C''(8, - 2 )
D'(1, - 6 ) → D''(1 + 4, - 6 + 1 ) → D''(5, - 5 )
These are the correct coordinates for the diagram A''B''C''D''
Hence the composition of transformations is correct
