Which coordinate system is used to determine a point's location using distance and angle?

The polar coordinate system is designed specifically to determine a point's location using a distance from a reference point (commonly the origin) and an angle measured from a reference direction (usually the positive x-axis). In this system, each point in a two-dimensional plane is represented uniquely by the pair (r, θ), where 'r' is the radial distance to the point and 'θ' is the angle relative to the reference direction.

Polar coordinates are particularly useful in scenarios where the relationship between points is more naturally described in terms of angles and distances, such as in circular or rotational symmetries. This contrasts with rectangular coordinates, which rely on horizontal and vertical distances from the axes, and are less effective for expressing circular relationships.

The cylindrical and spherical coordinate systems build on this concept but extend it to three-dimensional space. Cylindrical coordinates add a height component to the polar coordinates, while spherical coordinates utilize angles and a radius to locate points in a three-dimensional sphere. However, for the specific context of locating points using just distance and angle in a two-dimensional plane, the polar coordinate system is the correct choice.