Chapter Closure
Sign In
Let's start by considering the differences between the given figures.
Looking at the figures, we can see that there is a clear pattern. Each figure has 6 tiles more than the previous one. To graph the next figure, we draw one tile on the left side of the figure, one tile on the right side of the figure, two tiles in the left column, and two tiles in the right column. Let's add these tiles to Figure 3 to get Figure 4.
To graph Figure 0, we remove one tile from the left side, one tile from the right side, two tiles from the left column, and two tiles from the right column of Figure 1.
In Part A we sketched Figures 0 and 4.
We can graph all figures together.
Now we can compare all figures by making a table of number of tiles in each figure.
| Figure Number | Figure 0 | Figure 1 | Figure 2 | Figure 3 | Figure 4 |
|---|---|---|---|---|---|
| Number of Tiles | 5 | 11 | 17 | 23 | 29 |
We want to graph the number of tiles in each figure. Let's take a look at the table we made in Part B.
| Figure Number | Figure 0 | Figure 1 | Figure 2 | Figure 3 | Figure 4 |
|---|---|---|---|---|---|
| Number of Tiles | 5 | 11 | 17 | 23 | 29 |
Now we will graph each (x,y) point on the same coordinate plane.
Let's take a look at the number of tiles in each figure.
| Figure Number | Number of Tiles |
|---|---|
| 0 | 5 |
| 1 | 5+6=11 |
| 2 | 11+6=17 |
| 3 | 17+6=23 |
| 4 | 23+6=29 |
We can see that each figure has 6 tiles more than the previous figure. This means that the growth factor of the pattern is 6.