   Chapter 10.4, Problem 111E

Chapter
Section
Textbook Problem

# True or False? In Exercises 113-116, determine whether the statement is true or false. If it is false, explain why or give an example that shows it Is false.If ( r 1 , θ 1 ) and ( r 2 , θ 2 ) represent the same point on the polar coordinate system, then | r 1 | = | r 2 | .

To determine
Whether the given statement “If (r1,θ1) and (r2,θ2) represent the same point on the polar coordinate system, then |r1|=|r2|” is true or false.

Explanation

The point in the coordinate plane can be located in the form of polar coordinates (r,θ) in which r is directed distance from origin to the point and θ is directed angle that is taken counterclockwise from polar axis to the line segment and it is joining origin and the point.

As it is given that the same point is represented by two polar coordinates (r1,θ1) and (r2,θ2) The distance between the point and the origin is a constant.

Consider the distance be d.

Therefore |r1|=|r2|=d

Here, the modulus is taken because the distance between two points is always positive

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