To translate the points A, B, and C to their new locations A', B', and C', we use the functions f(x) = x + h and g(y) = y + k. Here, 'h' is the amount we move the x-coordinates, and 'k' is how much we move the y-coordinates.
By looking at the points, we see that A (1,-1) moves to A' (-7,-1), so h = -8 (1 to -7) and k = 0 (y stays the same). For point B (5,-2) moving to B' (-1,-4), we see h = -6 (5 to -1) and k = -2 (-2 to -4).
Lastly, point C (2,3) to C' (0,-3) shows us h = -2 (2 to 0) and k = -6 (3 to -3).
Since the amount we move in the x-direction is different for each point, we can say this translation is not the same for all points. Overall, we can see that the translations for each point are unique based on how far they move both horizontally and vertically!
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