To determine which point is the greatest distance from Point V, we can calculate the distance between Point V and each of the other points using the distance formula. The distance formula between two points (x1, y1) and (x2, y2) is given by:

Distance = √((x2 - x1)² + (y2 - y1)²).

For Point V (5, 1):
- Distance to Point W (5, -4): √((5 - 5)² + (-4 - 1)²) = √(0 + 25) = 5.
- Distance to Point X (5, 5): √((5 - 5)² + (5 - 1)²) = √(0 + 16) = 4.
- Distance to Point Y (8, 1): √((8 - 5)² + (1 - 1)²) = √(9 + 0) = 3.
- Distance to Point Z (-2, 1): √((-2 - 5)² + (1 - 1)²) = √(49 + 0) = 7.

Comparing these distances, Point Z is the farthest from Point V, with a distance of 7 units.