Question

In a quilt pattern, a polygon with vertices(-4,-2), (-3,-1), (-2, -2), and (-3, -3) is translated repeatedly along the vector (2, 2). What are the coordinates of the third polygon in the pattern? Explain how you solved the problem.

Answer 1

The polygon has vertices (-4,-2), (-3,-1), (-2,-2) and (-3,-3).

Note that translation along the vector (2,2) is equivalent to
(i) translation of 2 in the x-direction, and
(ii) translation of 2 in the y-direction.

Create a table to show how the coordinates change after each translation.
Translation
Number
-----------
1 (-4,-2) (-3,-1) (-2,-2) (-3,-3) Before
(-2,0) (-1,1) (0,0) (-1,-1) After

2 (0,2) (1,3) (2,2) (1,1) After

3 (2,4) (3,5) (4,4) (3,3) After

After n translations, each coordinate (x,y) changes into (x+2*n, y+2*n).
Therefore after 3 translations, each coordinate increases by 6.

Answer:
After 3 translations, the coordinates of the 3-rd polygon are
(2,4), (3,5), (4,4), and (3,3)