## Which set of polar coordinates describes the same location as the rectangular coordinates (1,-1) A. (-1, 135 degrees) <

Question

Which set of polar coordinates describes the same location as the rectangular coordinates (1,-1)

A. (-1, 135 degrees)
B. (sqrt 2, 315 degrees)
C. (1, 45 degrees)
D. (sqrt 2, 225 degrees)

in progress 0

The polar coordinate is [tex](sqrt{2},315^circ)[/tex]

B is correct

Step-by-step explanation:

Given:

Rectangular coordinates: (1,-1)

We need to change into polar coordinate.

Cartesian to polar change rule:

[tex](x,y)rightarrow (r,theta)[/tex]

[tex]x=rcostheta[/tex]

[tex]y=rsintheta[/tex]

[tex]text{Where, }r=sqrt{x^2+y^2}text{ and }theta=tan^{-1}dfrac{y}{x}[/tex]

[tex]=r=sqrt{1+1}=sqrt{2}[/tex]

[tex]sqrt{2}costheta=1[/tex]

[tex]sqrt{2}sintheta=-1[/tex]

Cosine is negative and Sine is positive.

Thus, angle lie in IV quadrant.

[tex]theta=tan^{-1}(-1)[/tex]

[tex]theta=360-45=315^circ[/tex]

Cartesian to polar

[tex](1,-1)rightarrow (sqrt{2},315^circ)[/tex]

Hence, The polar coordinate is [tex](sqrt{2},315^circ)[/tex]

2. The answer to this question is B. (sqrt 2, 315 degrees). This polar coordinate is the only coordinate with its angle in quadrant 4 and a length of u221a1^2 + (-1)^2 = u221a2.