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Two points in the Cartesian plane are A(2.00 m, −4.00 m) and B(−3.00 m, 3.00 m). Find the distance between them and their polar coordinates.

1 Answer

5 votes

The distance between the two points is
d=8.6m

The polar coordinate of A is
\left(4.47,296.57\right)

The polar coordinate of B is
\left(4.24,135\right)

Step-by-step explanation:

The two points are
A(2,-4) and
B(-3,3)

The distance between two points is given by,


d=\sqrt{(2+3)^(2)+(-4-3)^(2)}\\d=\sqrt{(5)^(2)+(-7)^(2)}\\d=√(25+49)\\d=8.6

Thus, the distance between the two points is
d=8.6m

The polar coordinates of A can be written as
(Distance, tan^(-1) (y)/(x) )

Distance =
\sqrt{x^(2) +y^(2) }

Substituting
A(2,-4), we get,

Distance =
\sqrt{2^(2) +(-4)^(2) }=√(4+16 )=4.47


tan^(-1) (y)/(x) =tan^(-1) (-4)/(2)=-63.43

To make the angle positive, let us add 360,


\theta=360-63.43=296.57

The polar coordinate of A is
\left(4.47,296.57\right)

Similarly, The polar coordinate of B can be written as
(Distance, tan^(-1) (y)/(x) )

Distance =
\sqrt{x^(2) +y^(2) }

Substituting
B(-3,3), we get,

Distance =
\sqrt{(3)^(2)+(3)^(2)}=4.24


tan^(-1) (y)/(x) =tan^(-1) (3)/(-3)=-45

To make the angle positive, let us add 360,


\theta=180-45=135^(\circ)

The polar coordinate of B is
\left(4.24,135\right)

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