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Consider point $A$ in the Cartesian plane below (the grid lines occur every unit):

 

[asy] size(200); import TrigMacros; rr_cartesian_axes(-7,7,-7,7,complexplane=false,usegrid=true); pair A = (2,3); dot(A, red+ linewidth(3.5)); label("$A$", A, S); [/asy]

 

Say that $A$ is at the polar coordinates of $(r, \theta)$. If the Cartesian coordinates of the point with polar coordinates $\left(2r, \theta + \pi/2 \right)$ are $(x_1, y_1),$ and the Cartesian coordinates of the point with polar coordinates $\left(-r, -\theta \right)$ are $(x_2, y_2)$, enter

 

\[x_1, y_1, x_2, y_2\]

 

in that order.

 Jul 30, 2021
 #1
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$(x_1, y_1, x_2, y_2) = (-4, 6, -3, -2)$

 Sep 12, 2021

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