Final answer:
Polar coordinates are converted to Cartesian coordinates using cosines and sines for x and y respectively. The distance between two Cartesian points is calculated with the distance formula. The slope of a line through two points is found by dividing the difference in y-coordinates by the difference in x-coordinates.
Step-by-step explanation:
To convert polar coordinates to Cartesian coordinates, we use the relations x = r × cos(θ) and y = r × sin(θ).
Example Conversion:
For point with polar coordinates (47/3, 5.50 m):
x = (47/3) × cos(5.50) and y = (47/3) × sin(5.50).
Calculating Distance:
To find the distance between two points in the Cartesian coordinate system, we can apply the distance formula: d = √((x2 - x1)^2 + (y2 - y1)^2).
Slope Calculation:
The slope of a line that passes through two points (x1, y1) and (x2, y2) is calculated by: slope = (y2 - y1) / (x2 - x1). For the given points (1, 0.1) and (7, 26.8), slope = (26.8 - 0.1) / (7 - 1).