Question

Convert the rectangular coordinates (2,-2) to polar form and find two additional polar representations of this point. Please Help!! Will give MEDAL!!

Answer 1

Do you know the basics of how to go from rectangular (Cartesian) coordinates to polar?

Answer 2

No

Answer 3

Alright, instead of having x and y coordinates, polar coordinates uses a radius and an angle. So, out first task is to find the length of the line that connects the origin (0,0) to our point (2,-2)

Answer 4

Do you know how to find that distance?

Answer 5

Not sure could you help ???

Answer 6

Sure. The distance between two points is:
\[r = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\]

Answer 7

Your two points are (0,0) and (2,-2). Plug the values into that equation, and find the radius.

Answer 8

r=2????

Answer 9

Not quite.

\[r = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(2-0)^2 + (-2-0)^2} = \sqrt{(2)^2+(-2)^2} = \sqrt{4+4} = \sqrt{8}\]

Answer 10

Ack

\[=\sqrt{8}\]

Answer 11

sqrt8=2.828??

Answer 12

Sounds about right, I'd probably leave it as sqrt(8), but your teacher may want a decimal.

Answer 13

Our next step is to find the angle. Do you know how to find the angle of a line from the origin to the point (2,-2)?

Answer 14

Not sure again my teacher didn't explain this

Answer 15

It's alright :)

Ok, so the two components of the point actually tell us the length of the sides of a triangle whose hypotenuse points straight to that point.

Our point is (2,-2), which will look like this: