Final answer:
Graphing triangle DEF involves plotting its vertices on a coordinate plane and connecting them. Translating the triangle requires adding the components of a vector to the vertices and plotting the new points to form the translated image of the triangle.
Step-by-step explanation:
To graph triangle DEF using the vertices D(2,5), E(6,3), and F(4,0), you would plot these points on a coordinate plane and connect them to form the triangle. A translation using a vector moves the triangle along a straight path from its initial position to a new position without changing its size, shape, or orientation.
To translate the triangle, you would add the vector's components to each of the vertices. If the translation vector were v = (x, y), you would then find the image of D by calculating D' = (2+x, 5+y), the image of E as E' = (6+x, 3+y), and the image of F as F' = (4+x, 0+y). Graphing these new vertices will give you the image of triangle DEF after the translation.