Question

Fill in the blanks to convert between rectangular coordinates and polar coordinates.

$r=...............$

Short answer

The value of$r=\sqrt{x^2+y^2}$

Step-by-step solution

Step 1. Given information

$r$is the distance of the point from the origin.

Step 2. Convert r into rectangular coordinate. 

Draw a diagram of a circle of radius $r$and let a pointlocalid="1652261998898" $P\left(x,y\right)$on the circle

Here in the right angle triangle we can apply Pythagorous theorem:

$$\begin{gathered} r^2=x^2+y^2 \\ r=\sqrt{x^2+y^2} \end{gathered}$$