Final answer:
The points (6,-8) and (-1,-8) are on a horizontal line, and the vectors from the origin to each point have the same magnitude but opposite directions, thus are not equal vectors. The displacement between these two points is equal in magnitude.
Step-by-step explanation:
The given points (6,-8) and (-1,-8) suggest a question related to vector equality or the properties of lines in coordinate geometry. When two points share the same y-coordinate but have different x-coordinates, as in this case, the line connecting them is horizontal and parallel to the x-axis. Thus, they have no vertical change (no change in the y-coordinate), which implies that the segment connecting these points is a horizontal line with a slope of zero.
Speaking in terms of vectors, if we were to form vectors from the origin to each point, their resulting vectors would be equal if they have the same magnitude and direction. Since the y-components of both vectors are the same and the x-components only differ by their signs, the vectors have equal magnitude but opposite directions, therefore they are not equal vectors.
Moreover, if the reference to 'equal' pertains to the magnitude of the displacement between these points, they would indeed be equal since they lie on the same horizontal line, implying that the displacement in the y-direction is zero and the displacement in the x-direction is the difference between the x-coordinates of the two points, regardless of the order.