## How to Read Off the Polar Coordinates a Point

Reading off the polar coordinates of a point is easy.## Question

What are the polar coordinates of the point shown on the graph below.## Step-by-Step:

## 1

Draw a line from the pole to the point.

**Don't forget:**In polar coordinates, there is a reference point (called the**pole**) and a reference direction shown by the horizontal**polar axis**.## 2

Find the length of this line.

- Use a ruler with the same scale as the polar axis:

- Use a compass. With the compass needle on the pole, draw an arc through the point to the polar axis:

**5**.**5 is the radial coordinate of the point.**## 3

Measure the angle of the line from the polar axis (in the counter-clockwise direction).

The angle is

The angle is

**45°**.**45° is the angular coordinate of the point.**## 4

Write down the polar coordinates as a pair of numbers in brackets, separated by a comma.
The radial coordinate (

**5**) found in**Step 2**goes on the left. The angular coordinate (**45°**) found in**Step 3**goes on the right.## Answer:

## Reading Off Point from Polar Coordinates Using the Polar Grid

A polar grid helps us draw a point from polar coordinates.- The concentric circles show us points with the same radial coordinate (because the circles have the same radius).
- The straight lines show us points with the same angular coordinate (because all points on the line are the same angle from the polar axis).

**5**and on the line at an angle of

**45°**.

We can read off the polar coordinates as

**(5, 45°)**.

## What's in a Name?

Polar coordinates are named because Jacob Bernoulli called the point from which other points are measured the**pole**and the horizontal line which passes through it the

**polar axis**. The radial coordinate is sometimes called the

**radius**. The angular coordinate is sometimes called the

**polar angle**or the

**azimuth**.

## Why Are Polar Coordinates Useful?

Polar coordinates are useful when dealing with circular geometry. All the points that can be drawn on a circumference of a circle have the same radius, but lie at difference angles. For example, a circle of radius 2:## You might also like...

graphs and coordinate geometrydrawing a point from Cartesian coordinatesconverting from Cartesian to polar coordinatesconverting from polar to Cartesian coordinates

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