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How do you convert #( -2x , -2y )# into polar coordinates?

Answer 1

Serenity Johnson

For #r#: #r^2=x^2+y^2#

#r^2=(-2x)^2+(-2y)^2#

#r^2=4x^2+4y^2#

#r=2sqrt(x^2+y^2)#

For #theta#: #theta=tan^(-1)(y/x)#

#theta=tan^-1 ((cancel(-2)y)/(cancel(-2)x))#

#theta=tan^-1 (y/x)#

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Answer 2

Sophie Adams

To convert from rectangular coordinates to polar coordinates, we use the following formulas:

[ r = \sqrt{x^2 + y^2} ] [ \theta = \arctan\left(\frac{y}{x}\right) ]

For the point (-2x, -2y), we first find the values of x and y:

[ x = -2x ] [ y = -2y ]

Then, we substitute these values into the formulas:

[ r = \sqrt{(-2x)^2 + (-2y)^2} = \sqrt{4x^2 + 4y^2} = 2\sqrt{x^2 + y^2} ] [ \theta = \arctan\left(\frac{-2y}{-2x}\right) = \arctan\left(\frac{y}{x}\right) ]

So, the polar coordinates for the point (-2x, -2y) are ( (2\sqrt{x^2 + y^2}, \arctan(y/x)) ).

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Answer from HIX Tutor

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