Final answer:
To combine the translations (T-3, 4) and (T18,-7) into one, simply add their respective x and y components, resulting in the single translation (T15, -3).
Step-by-step explanation:
The student is asking how to combine two translations, (T-3, 4) and (T18,-7), into a single translation. The notation (Tx, Ty) represents a translation that shifts a point in the plane by Tx units in the x-direction and Ty units in the y-direction. To combine two translations, we add their respective components. Thus:
(T-3, 4) · (T18,-7) = (T(-3+18), T(4-7))
This results in the single translation:
(T15, -3)
In this combined translation, every point in the plane would move 15 units to the right and 3 units down. This simplification is based on vector addition, where translations can be thought of as vectors with their x and y components representing the movement in each direction.