Question

Two points in a plane have polar coordinates (2.10m, 40.0 degrees ) and (3.90m, 110.0 degrees ) a. Determine the Cartesian coordinates of these points b. Determine the distance between them

Answer 1

To convert polar coordinates to Cartesian coordinates, we can use the formulas x = r * cos(θ) and y = r * sin(θ). For the given points (2.10 m, 40.0 degrees) and (3.90 m, 110.0 degrees), the Cartesian coordinates are (1.6 m, 1.3 m) and (-0.9 m, 3.5 m) respectively. The distance between the two points is approximately 3.83 m.

Step-by-step explanation:

To determine the Cartesian coordinates of points given in polar coordinates, we can use the formulas:

x = r * cos(θ)

y = r * sin(θ)

For point A, the Cartesian coordinates are:

x = (2.10 m) * cos(40.0 degrees) = 1.6 m

y = (2.10 m) * sin(40.0 degrees) = 1.3 m

So, the Cartesian coordinates of point A are (1.6 m, 1.3 m).

For point B, the Cartesian coordinates are:

x = (3.90 m) * cos(110.0 degrees) = -0.9 m

y = (3.90 m) * sin(110.0 degrees) = 3.5 m

So, the Cartesian coordinates of point B are (-0.9 m, 3.5 m).

To determine the distance between the points, we can use the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Plugging in the coordinates of points A and B:

d = sqrt((1.6 m - (-0.9 m))^2 + (1.3 m - 3.5 m)^2) = sqrt(9.625 m^2 + 5.04 m^2) = sqrt(14.665 m^2) ≈ 3.83 m