Final answer:
The vector that translates point A(-2, 7) to A'(6, 4) is found by subtracting A from A', resulting in the translation vector (8, -3).
Step-by-step explanation:
To find the vector that translates point A(-2, 7) to A'(6, 4), we need to determine the vector that, when added to point A, gives us point A'. This vector is often called the translation vector. The translation vector ⇒T can be found by subtracting the coordinates of A from the coordinates of A'.
⇒T = A' - A
⇒T = (6, 4) - (-2, 7)
⇒T = (6 - (-2), 4 - 7)
⇒T = (6 + 2, 4 - 7)
⇒T = (8, -3)
Therefore, the translation vector ⇒T is (8, -3), which means that to move from point A to A', we will move 8 units in the x-direction and -3 units in the y-direction.