Final answer:
The question requires converting polar coordinates to Cartesian coordinates and finding the distance between two points in the Cartesian coordinate system.
Step-by-step explanation:
The question involves finding all polar coordinates of a given point as well as converting polar coordinates to Cartesian coordinates. The polar coordinates are expressed in terms of a radius and an angle, usually designated as (r, θ). To express a point with polar coordinates in the Cartesian plane, we use the relations x = r × cos(θ) and y = r × sin(θ). For the point P (2.500 m, π/6), converting into Cartesian coordinates yields x = 2.165 m and y = 1.250 m. Similarly, point P₂ (3.800 m, 27/3) in Cartesian coordinates is x = -1.900 m and y = 3.290 m. The distance between these two points in the Cartesian plane can be calculated using the distance formula √((x2 - x1)² + (y2 - y1)²), which gives approximately 5.27 m (rounded to the nearest centimeter).