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)