Given that p = (2, 9) and q = (4, 14), find the component form and magnitude of vector pq.

We are asked to determine the lengths of the line segment drawn with these points as endpoints. The equation of the distance between points is,
                              d = sqrt ((y2 - y1)² + (x2 - x1)²)
Substituting the coordinates of the points,
                               d = sqrt ((14 - 9)² + (4 - 2)²)
The numerical value for d is approximately 5.39.