Step-by-step explanation:
2.
an isometry means the distance between any two points in the original space is the same as the distance between them in the second space.
rotation and translation are such isometries. they leave the original shape or curve unchanged in its inner structure but move it around.
so, the shapes in this question are visibly an isometry. the size and structure of the pre-image is the same as for the image. only its position changed.
4.
(x, y) -> (x-3, y+5) means that every point of the shape or curve is moved (translated) 3 units to the left (the x coordinate is decreased) and 5 units up (the y coordinate is increased).
6.
(x, y) -> (x+7, y-2) -> (x-3, y+2)
this means that first every point of the shape or curve is moved (translated) 7 units to the right and 2 units down, and then 3 units to the left and 2 units up.
in the end this means that every point moved 4 units to the right (no up or down changes, as the intermediate changes canceled each other out).
