Final answer:
The coordinates of point A are (2.00 m, -4.00 m). To convert between Cartesian and polar coordinates, use x = r * cos(θ) and y = r * sin(θ), and for polar use √(x² + y²) and atan2(y, x) to find the radius and angle respectively. The distance between two points in a Cartesian plane is found using the distance formula.
Step-by-step explanation:
To determine the coordinates of point A, we need to reference a Cartesian coordinate system, where each point is represented as (x, y) and can be extended to 3D as (x, y, z). In the context of the provided information, the coordinates of point A are given as (2.00 m, -4.00 m). If we need to find the distance between two points A and B in a Cartesian plane, we would use the distance formula which is the square root of the sum of the squares of the differences in x-coordinates and y-coordinates of points A and B respectively.
For converting polar coordinates to Cartesian coordinates, we use the formulas x = r * cos(θ) for the x-coordinate, and y = r * sin(θ) for the y-coordinate, where 'r' is the radius (distance from the origin) and 'θ' (theta) is the angle in radians from the positive x-axis. Vice versa, to find polar coordinates from Cartesian coordinates, we find the radius using the Pythagorean theorem (√(x² + y²)) and the angle θ using the arctangent function (atan2(y, x)).
For example, given polar coordinates (2.500 m, π/6) and (3.800 m, 2π/3), we can find Cartesian coordinates for each point and then calculate the distance between them in the Cartesian coordinate system.