Convert the point to polar coordinates.
$(-2,2)$

• A. $(2\(\sqrt{2}\),\(\frac{3\pi}{4}\))$
• B. $(2\(\sqrt{2}\),-\(\frac{\pi}{4}\))$
• C. $(2\(\sqrt{2}\),\(\frac{\pi}{4}\))$
• D. $(-2\(\sqrt{2}\),\(\frac{3\pi}{4}\))$

Answer: (A)

Verified step by step guidance

1. To convert a point from Cartesian coordinates (x, y) to polar coordinates (r, θ), we use the formulas: r = \(\sqrt{x^2 + y^2}\) and θ = \(\arctan\[\left\)(\(\frac{y}{x}\]\right\)).
2. For the point (-2, 2), calculate the radius r: r = \(\sqrt{(-2)^2 + 2^2}\) = \(\sqrt{4 + 4}\) = \(\sqrt{8}\) = 2\(\sqrt{2}\).
3. Next, calculate the angle θ using the arctangent function: θ = \(\arctan\[\left\)(\(\frac{2}{-2}\]\right\)) = \(\arctan\)(-1).
4. Since the point (-2, 2) is in the second quadrant, the angle θ should be adjusted to reflect this. The reference angle for \(\arctan\)(-1) is \(\frac{\pi}{4}\), so in the second quadrant, θ = \(\pi\) - \(\frac{\pi}{4}\) = \(\frac{3\pi}{4}\).
5. Thus, the polar coordinates for the point (-2, 2) are (2\(\sqrt{2}\), \(\frac{3\pi}{4}\)).