In a city, a person gets from one place to another by following the grid formed by the city’s streets.
Before the city was there, however, the homesteader got from place to place by going a certain distance in a certain direction.
The city street grid is similar to the rectangular coordinate system, where points in the plane are designated by ordered pairs (x, y).
The homesteader used a system similar to polar coordinates, which also use ordered pairs,
but where the first element of the ordered pair (r, θ) is the distance to be covered and the second element specifies the direction, an angle measured from the positive x-axis.
This simulation allows you to experiment with the polar coordinate system and conversions to and from the rectangular coordinate system.
Enter the x and y values of a point and click the button that says Convert to polar coordinates. The polar coordinates of the point will appear in the boxes beneath the words polar coordinates …
… and the point will be plotted in a polar coordinate system grid. You can change from polar coordinates to rectangular as well.
Enter the polar coordinates of a point and click the Convert to rectangular coordinates button. The rectangular coordinates of the point will appear in the boxes beneath the words rectangular coordinates …
… and the point will be plotted in a rectangular coordinate system grid.
As you use the simulation and work through the explorations and exercises, try to predict the result before clicking the Convert button. Look for patterns and see if you verbalize generalizations. Happy exploring!