Given the rectangular coordinates (2,-2), which of the following polar coordinate pairs, in radians, represent the same point?

Answer A

Using Polar Coordinates we mark a point by how far away, and what angle it is.

To find polar co ordinates, When we know a point in Cartesian Coordinates (x,y) and we want it in Polar Coordinates (r,θ) we solve a right triangle with two known sides(2,-2)

using Pythagoras theorem,

base^2 + altitude ^ 2 = hypotenuse ^2

2^2 +(-2)^2 = hypotenuse

Hypotenuse = 2√2

to find angle we can use tan(angle) = altitude / base = (-2/2) = -1

so angle can be 3π/4 or 7π/4

as per the given options,

answer is 2√2,7π/4

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