Physics
posted by Vivian .
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?

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 36063.4 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. 
Theta =tan^5/5=45
R=Seq5+5=7.0