Final answer:
To find the set of points yielding the vector (AB) = (-6,1), select any starting point A (x1, y1) and calculate point B (x2, y2) using the vector components as the differences between the coordinates: x2 - x1 = -6 and y2 - y1 = 1.
Step-by-step explanation:
To find the set of points that yields the vector (AB) = (-6,1), we can utilize the concept that a vector represents the difference between its endpoints. Mathematically, if we have points A (x1, y1) and B (x2, y2), the vector (AB) can be found using the formula:
(AB) = (x2 - x1, y2 - y1)
In this case, we are given the vector (AB) = (-6,1), which means that:
There can be many pairs of points that satisfy this condition. For instance, if we choose point A to be at the origin (0, 0), then point B would need to be at (-6, 1) to give the vector (-6, 1). Alternatively, if we choose point A to be at (5, 4), then point B would be at (-1, 5).
The important idea to remember about vector subtraction is that it involves adding the negative of one vector to another, and the order of subtraction does not affect the results.