Final answer:
To find the vector a with representation given by the directed line segment ab, subtract the coordinates of point a from point b. The resulting vector has components (5, 9).
Step-by-step explanation:
To find a vector a with representation given by the directed line segment ab, we subtract the coordinates of point a from point b. Point a has coordinates (-4, -4) and point b has coordinates (1, 5). Subtracting the x-coordinates and the y-coordinates separately, we get a vector with components (1 - (-4), 5 - (-4)). Simplifying, we get a vector with components (5, 9). Therefore, the vector a has representation (5, 9).