Answer
The final coordinates are
G" (3, 3)
H" (7, 7)
S" (-1, 9)
Step-by-step explanation
To solve this, we need to note that
D₂ represents a dilation by a scale factor of 2
A dilation means the size is increased or decreased. If the scale factor is less than 1, then the size is decreased, but if the scale factor is more than 1, it means the figure is enlarged.
Dilating about the origin just multiplies the coordinates by the scale factor. So, dilating (x, y) about the origin by a scale factor k, gives new coordinates (kx, ky).
For our question,
G (3, 1) becomes G' [2(3), 2(1)] = G' (6, 2)
H (5, 3) becomes H' [2(5), 2(3)] = H' (10, 6)
S (1, 4) becomes S' [2(1), 2(4)] = S' (2, 8)
Then, the next transformation, T₋₃ ₁ means we add (-3) to the x-coordinate and (1) to the y-coordinate.
G' (6, 2) becomes G" [(6 - 3), (2 + 1)] = G" (3, 3)
H' (10, 6) becomes H" [(10 - 3), (6 + 1)] = H" (7, 7)
S' (2, 8) becomes S" [(2 - 3), (8 + 1)] = S" (-1, 9)
Hope this Helps!!!