A certain shing vessel is initially located in a horizontal plane at x = 0 and y = 10 mi. It moves on a path for 10 hr such that x = t and y = 0.5t² + 10, where t is in hours. An international shing boundary is described by the line y = 2x + 6.

a. Plot and label the path of the vessel and the boundary.

b. The perpendicular distance of the point (x₁, y₁) from the line Ax + By + C = 0 is given by

 

where the sign is chosen to make d ≥ 0. Use this result to plot the distance of the shing vessel from the shing boundary as a function of time for 0 ≤ t ≤ 10 hr.

Ax + By + C d = + VA? + B?