Question

The pair of coordinates that do not represent the point (5, 150º) is_______

5,-210
5,210
-5,330
-5,-30

Answer 1

(5,210)

Explanation:

(5,150°) is equivalent to (5,150-360) or (5,-210°)

and (5,150+360) or (5,510°)

also (5,150°) is equivalent to (-5,150+180)or (-5,330°)

and (-5,150-180) or (-5,-30°)

so (5,210) does not represent the given point.

Answer 2

Option B.

Explanation:

If a polar coordinate is defined as (r,θ) , then all polar coordinates of given point are (r, θ +2nπ) and (-r, θ+(2n+1)π), where n is an integer.

In degree if a point is (r,θ), then all polar coordinates of given point are (r, θ +360n) and (-r, θ+180n) where n is an integer.

The given pair of polar coordinates are (5, 150º). The different ways to write the given point are

(r, θ) = (r, θ +360n)

`(5,150^(\circ))=(5,150^(\circ)-360^(\circ))=(5,-210^(\circ))`

`(5,150^(\circ))=(5,150^(\circ)+360^(\circ))=(5,510^(\circ))`

(r, θ) = (r, θ +180n)

`(5,150^(\circ))=(-5,150^(\circ)-180^(\circ))=(-5,-30^(\circ))`

`(5,150^(\circ))=(-5,150^(\circ)+180^(\circ))=(-5,330^(\circ))`

The pair of coordinates that do not represent the point (5, 150º) is (5,210º).

Therefore, the correct option is B.