What is the distance between the following polar coordinates?: (1,pi), (4,pi) (1,π),(4,π)

1 Answer
Jan 4, 2018

See a solution process below:

Explanation:

The formula for the distance between two polar coordinates is:

d = sqrt(r_1^2 + r_2^2 - 2r_1r_2cos(Theta_1 - Theta_2))

Where the two points are (r_1, Theta_1) and (r_2, Theta_2)

Substituting the values from the points in the problem gives:

d = sqrt(1^2 + 4^2 - (2 xx 1 xx 4)cos(pi - pi))

d = sqrt(1 + 16 - 8cos(0))

d = sqrt(17 - (8 xx 1))

d = sqrt(17 - 8)

d = sqrt(9)

d = 3

The distance between the two points is 3 units.