Posted by **Vivian** on Wednesday, January 13, 2010 at 1:40pm.

Two points in the xy plane have Cartesian coordinates (2.00, -4.00) m and (-5.00, 5.00) m.

(a)What is the distance between these two points?

(b) What are their polar coordinates?

- Physics -
**Damon**, Wednesday, January 13, 2010 at 2:18pm
Difference in x = -5.00 -2.00 = -7

Difference in y = 5.00 - -4.00 = 9

hypotenuse = sqrt (49 +81) = sqrt(130)=11.40

so the distance is 11.40 meters

graph (2,-4)

that is in quadrant 4

it is 4 units below the x axis and two o the right of the y axis

tangent of angle below x axis = -4/2 = -2

tan^-1(2) = 63.4

so 63.4 degrees below x axis or 360-63.4 counterclockwise from x axis

so theta = 296.6 degrees or 5.18 radians

r = sqrt (2^2 + -4^2) = sqrt 20 = 2sqrt5

so first point in r theta is

r = 2 sqrt 5

theta = 5.18 radians or 296.6 degrees

Find r, theta for the second point the same way.

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