What is the distance between (3 ,( 5 pi)/12 ) and (-2 , ( 3 pi )/2 )?

1 Answer
Jun 20, 2016

The distance between the two points is approximately 1.18 units.

Explanation:

You can find the distance between two points using the Pythagorean theorem c^2 = a^2 + b^2, where c is the distance between the points (this is what you're looking for), a is the distance between the points in the x direction and b is the distance between the points in the y direction.

To find the distance between the points in the x and y directions, first convert the polar co-ordinates you have here, in form (r,\theta), to Cartesian co-ordinates.

The equations that transform between polar and Cartesian co-ordinates are:

x = r cos\theta
y = r sin \theta

Converting the first point
x = 3 cos(\frac{5\pi}{12})
x = 0.77646

y = 3 sin (\frac{5\pi}{12})
y = 2.8978

Cartesian co-ordinate of first point: (0.776, 2.90)

Converting the second point
x = -2 cos(\frac{3\pi}{2})
x = 0

y = -2 sin (\frac{3\pi}{2})
y = 2

Cartesian co-ordinate of first point: (0, 2)

Calculating a
Distance in the x direction is therefore 0.776-0 = 0.776

Calculating b
Distance in the y direction is therefore 2.90-2 = 0.90

Calculating c
Distance between the two points is therefore c, where
c^2 = a^2 + b^2
c^2 = 0.776^2 + 0.9^2
c^2 = 1.4122
c = 1.1884
c \approx 1.18

The distance between the two points is approximately 1.18 units.

The diagrams about halfway down this page, in the section 'Vector addition using components' might be useful in understanding the process just performed.