Final answer:
The algebraic description of the translation is (x, y) → (x + 4, y - 3), found by determining the change in the coordinates of the points M and T to their corresponding primes M' and T'.
Step-by-step explanation:
The question involves finding the translation vector that maps points M to M' and T to T' in the Cartesian plane. The translation vector (h, k) can be determined by the change in the x-coordinates and the y-coordinates of the given points. For point M, the x-coordinate changes from 3 to 7, which is a change of 4 units. The y-coordinate changes from 4 to 1, which is a change of -3 units. Therefore, the translation vector is (4, -3).
Thus, the algebraic description of this translation would complete the given equation to be:
(x, y) → (x + 4, y - 3)
We can apply the same process to point T to verify the translation vector. The x-coordinate changes from -2 to 2, and the y-coordinate changes from 3 to 0, which indeed confirms the translation vector as (4, -3).