a) In order to perform the translation (x, y) -> (x + 7, y - 5) we just have to add 7 to the x-coordinates of each point and subtract 5 from the y-coordinates of each point, like this:
G(-1, 6) -> G'(-1 + 7, 6 - 5) = G'(6, 1)
H(-1, 3) -> H'(-1 + 7, 3 - 5) = H'(6, -2)
I(-6, 6) -> I'(-6 + 7, 6 - 5) = I'(1, 1)
By plotting the points G'(6, 1), H'(6, -2) and I'(1, 1), we get:
b) In order to perform the refection through the line y = -3, we just have to subtract the y-coordinate of each point from -3, like this:
G'(6, 1) -> G'(6, -3 - 1) = G'(6, -4)
H'(6, -2) -> H'(6, -3 - (-2)) = H'(6, -1)
I'(1, 1) -> I'(1, -3 - 1) = I'(1, -4)
Then, the points we get after these transformations are G'(6, -4), H'(6, -1), and I'(1, -4)