Final answer:
The points (4, π/4) and (-4, -π/4) represent the same location in polar coordinates but are different points in Cartesian coordinates. Option d is correct.
Step-by-step explanation:
The points (4, π/4) and (-4, -π/4) represent different points in the Cartesian coordinate system but the same point in polar coordinates. In polar coordinates, a negative radius can be understood as reversing the direction from the origin, and an angle with a negative value indicates rotation in the opposite direction (clockwise).
Therefore, if you consider a point at (r, θ) in polar coordinates and then a point at (-r, -θ), they will end up being at the same location after accounting for the direction reversal given by the negative radius and the angle's direction.
To be clearer, the point (4, π/4) in polar coordinates converts to a Cartesian point with positive x and y coordinates. The point (-4, -π/4) suggests a movement in the reverse direction both radially and angularly, ending up at the same Cartesian coordinates as the point (4, π/4). So answer option d is correct.