Problem

The rectangular coordinates of a point are $(-10,0)$. Find the polar coordinates.

The polar coordinates for the point with positive $r$ can be given by (Type an ordered pair. Use angle measures greater than or equal to 0 and less than $2 \pi$.)

Answer

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Answer

Final Answer: The polar coordinates of the point $(-10,0)$ are \(\boxed{(10, \pi)}\).

Steps

Step 1 :The rectangular coordinates of a point are $(-10,0)$. We are asked to find the polar coordinates.

Step 2 :The polar coordinates of a point in the plane are given by $(r, \theta)$ where $r$ is the distance from the origin to the point and $\theta$ is the angle formed by the positive x-axis and the line segment connecting the origin to the point.

Step 3 :In this case, the point is $(-10,0)$, which lies on the negative x-axis. The distance from the origin to the point is $10$ (the absolute value of $-10$), and the angle formed by the positive x-axis and the line segment connecting the origin to the point is $\pi$ (or $180^\circ$) because the point lies on the negative x-axis.

Step 4 :So, the polar coordinates of the point $(-10,0)$ are $(10, \pi)$.

Step 5 :Final Answer: The polar coordinates of the point $(-10,0)$ are \(\boxed{(10, \pi)}\).

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