Question

Two points in the xy plane have cartesian coordinates (2.00, 24.00) m and (23.00, 3.00) m. determine (a) the distance between these points and (b) their polar coordinates

Answer 1

Part A:

The distance between two points can be calculated through the equation,
         d = sqrt ((x₂ - x₁)² + (y₂ - y₁)²)

Each of the point may take the 1st or the 2nd coordinates. Substituting the known values,
        d = sqrt ((23 - 2)² + (3 - 24)²)
        d = 21√2
        d = 29.7

Part B:
We get the angle between the lines generated from points and the origin. 

Angle 1: θ = tan⁻(3/23) = 7.43°
Angle 2: θ = tan⁻(24/2) = 85.24°

Subtracting the values,
Angle = 77.8°

Thus, the polar coordinate is (29.7, 77.8°).