Question

Which set of polar coordinates describes the same location as the rectangular coordinates (0,-2)? A. (-2,270) B. (2,0) C. (2,180) D. (-2,90)

Answer 1

The correct polar coordinates for the rectangular coordinates (0, -2) are (2, 270°), representing a radius of 2 and an angle of 270 degrees from the positive x-axis.

Step-by-step explanation:

The question asks which set of polar coordinates describes the same location as the rectangular coordinates (0,-2). To find the correct polar coordinates, we use the transformation from rectangular to polar coordinates, which involves finding the radius r and the angle θ.

The radius r is calculated as the distance from the origin to the point, which can be found using the Pythagorean theorem. Since the point is on the y-axis, r is simply the absolute value of the y-coordinate, which is 2.

The angle θ represents the direction of the radius with respect to the positive x-axis. For a point on the negative y-axis, this angle is 270 degrees (or π/2 radians if using radian measure).

Therefore, the polar coordinates that describe the same location as (0, -2) in rectangular coordinates are (2, 270°), which corresponds to option A: (-2, 270).

Answer 2

Polar coordinate is written in the form (
`r`,Θ°), where


`r= \sqrt{x^(2)+ y^(2) }`
Θ=
`tan^(-1) ( (y)/(x) )`

Θ is the angle formed between the side 'r' and the horizontal line as shown in the diagram below.

We have the cartesian coordinate (0, -2) with x=0 and y=-2


`r = \sqrt{0^(2) + (-2)^(2) } = √(4) =2`

For the coordinate (0, -2) there is no angle formed between the line and horizontal line, so Θ=0

Hence the polar coordinate is (2, 0°)