Chapter Closure
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To enlarge the polygon by a factor of 3, we have to triple the distance of each vertex from the origin and in the same direction. We can do this if we multiply each point's coordinates by 3.
| (x,y) | (3x,3y) | = |
|---|---|---|
| (- 1,1) | ( 3(- 1), 3(1)) | (- 3,3) |
| (5,1) | ( 3(5), 3(1)) | (15,3) |
| (5,- 1) | ( 3(5), 3(- 1)) | (15,- 3) |
| (1,- 1) | ( 3(1), 3(- 1)) | (3,- 3) |
| (1,- 3) | ( 3(1), 3(- 3)) | (3,- 9) |
| (- 5,- 3) | ( 3(- 5), 3(- 3)) | (- 15,- 9) |
| (- 5,3) | ( 3(- 5), 3(3)) | (- 15,9) |
| (- 3,3) | ( 3(- 3), 3(3)) | (- 9,9) |
| (- 3,- 1) | ( 3(- 3), 3(- 1)) | (- 9,- 3) |
| (- 1,- 1) | ( 3(- 1), 3(- 1)) | (- 3,- 3) |
Now we can draw the dilated polygon.
| (x,y) | (1/2x,1/2y) | = |
|---|---|---|
| (- 3,3) | ( 1/2(- 3), 1/2(3)) | (- 1.5,1.5) |
| (15,3) | ( 1/2(15), 1/2(3)) | (7.5,1.5) |
| (15,- 3) | ( 1/2(15), 1/2(- 3)) | (7.5,- 1.5) |
| (3,- 3) | ( 1/2(3), 1/2(- 3)) | (1.5,- 1.5) |
| (3,- 9) | ( 1/2(3), 1/2(- 9)) | (1.5,- 4.5) |
| (- 15,- 9) | ( 1/2(- 15), 1/2(- 9)) | (- 7.5,- 4.5) |
| (- 15,9) | ( 1/2(- 15), 1/2(9)) | (- 7.5,4.5) |
| (- 9,9) | ( 1/2(- 9), 1/2(9)) | (- 4.5,4.5) |
| (- 9,- 3) | ( 1/2(- 9), 1/2(- 3)) | (- 4.5,- 1.5) |
| (- 3,- 3) | ( 1/2(- 3), 1/2(- 3)) | (- 1.5,- 1.5) |
With this, we can plot the shrunken polygon.
