The single transformation that took place from their starting position to their final destination is (x, y) ⇒ (x + 7, y)
What is transformation?
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
Translation is the movement of a point either up, down, left or right in the coordinate plane.
Hikers walk 3 miles east and then 2 miles north and take a water break. Hence:
(x, y) ⇒ (x + 3, y + 2)
They continue hiking 4 miles east and a final 2 miles south to their destination:
(x, y) ⇒ (x + 3 + 4, y + 2 - 2) ⇒ (x + 7, y)
The single transformation that took place from their starting position to their final destination is (x, y) ⇒ (x + 7, y)