Final answer:
A translation T(3,4) moves a figure 3 units right and 4 units up. Applying this to the line segment from (0,2) to (3,2) results in a new segment from (3,6) to (6,6).
Step-by-step explanation:
The student is asking about a mathematical concept known as translation. A translation in mathematics is a type of transformation that moves every point of a shape or figure the same distance in the same direction.
In this case, the student is asked to graph the image of a figure under the translation T(3,4), which means moving the figure 3 units to the right and 4 units up.
To apply the translation T(3,4) to the given line segment that goes from (0,2) to (3,2), we add 3 to the x-coordinates and 4 to the y-coordinates of each endpoint. After the translation, the new coordinates will be (0+3, 2+4), which is (3, 6) for the first point, and (3+3, 2+4) or (6, 6) for the second point.
Thus, the new line segment after the translation will go from (3, 6) to (6, 6), and will still be horizontal since the y-coordinates of both new endpoints are equal.