Activity A.1.2.
In this activity, we look at how transform the coordinates of points when changing the scale of your coordinate system.
While walking your dog, you notice that your dog takes three steps for every step of yours. When you sit down at home you realize that your coordinate system for your house is different than your dog’s. You decide to make the origin of both your coordinate system and your dog’s to be the entrance to your kitchen. Your dog’s bed is eight of your steps south and four steps west of the entrance to the kitchen. The dog’s water bowl is 5 of your steps north and 3 steps east from the entrace to your kitchen. The front door of your house is 15 of your steps south and 9 steps east of the entrance to the kitchen.
(a)
Draw a set of axes and plot the location of your dog’s bed, water bowl, and the front door in terms of your steps from the origin (the entrance to your kitchen).
(b)
State what the coordinates of your dog’s bed, water bowl, and the front door in terms of your dog’s steps from the origin will be.
(c)
If your dog’s favorite toy is 17 dog steps east and 5 dog steps north of the entrance to the kitchen and your dog’s collar is 13 dog steps south and 7 dog steps west, give the coordinates of your dog’s toy and collar in terms of your steps.
(d)
If you call the coordinates in your steps the \((x,y)\)-coordinate system and refer to coordinates in your dog’s steps as the \((x',y')\)-coordinate system, give the location in both coordinate systems for your dog’s bed, water bowl, the front door, your dog’s favorite toy, and your dog’s collar.
(e)
Generalize your findings from the previous part into equations that tranform between \((x,y)\)- and \((x',y')\)-coordinates.
