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?
(a)What is the distance between these two points?
(b) What are their polar coordinates?
Answers
Damon
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.
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.
Yakeen
Theta =tan^5/-5=-45
R=Seq5+5=7.0
R=Seq5+5=7.0