Question

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?

Answer 1

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.

Answer 2

Theta =tan^5/-5=-45
R=Seq5+5=7.0