Question

Which of the following ordered pairs below represents the same point in space in both the cartesian coordinate system and the polar coordinate system

Answer 1

Recall that in polar coordinates, the first entry represents the radius, and the second entry of the ordered pair represents the angle:

`(r,\theta).`

Now, in Cartesian coordinates, the first entry represents how much you "move" in the x, axis the second entry represents how much you "move" in the y-axis.

Therefore, a point that is the same in both coordinates, can have the same first entry, but we have to be careful with the second entry, from the given options, notice that the point:

`(\pi,0)`

represents the same point on the plane for both coordinate systems.

Answer:

`(\pi,0).`