Final answer:
To find the coordinate of point C, add the vector BC to the coordinate of point B. By adding 4 to the x-coordinate of B and subtracting 7 from the y-coordinate, we find that C is at (5, -4).
Step-by-step explanation:
To find the coordinates of point C given that the distance from B to C is represented by the vector (4, -7), and we know the coordinates of point B(1, 3), we need to add the vector to point B's coordinates. The operation we use is vector addition, where we add corresponding components. That means we add 4 to the x-coordinate of B and -7 to the y-coordinate of B.
The calculation is as follows:
x-coordinate of C: 1 + 4 = 5
y-coordinate of C: 3 - 7 = -4
Therefore, the coordinates of point C are (5, -4).