Final answer:
The question relates to geometry and algebra concepts within the Cartesian coordinate system, involving points and lines. It is mathematical in nature and suitable for students at the high school level.
Step-by-step explanation:
The question involves finding properties and relationships between points and lines in the Cartesian coordinate system. We can understand from the provided information that line ℓ contains points (-2, 1) and (4, 1), which suggests this is a horizontal line since the y-coordinate for both points is the same.
Point P has coordinates (5, 7) and is therefore not on line ℓ. One might also seek to find the slope of line ℓ, determine the equation of a line parallel or perpendicular to it, or calculate the distance from point P to line ℓ. However, these operations are not explicitly requested in the question.
The question is mathematical since it deals with concepts such as point and line placement in a two-dimensional plane, line properties, and distance calculations. It involves understanding the principles of geometry and algebra that are typically covered in the high school curriculum.