Final answer:
To find the original coordinates of point N, we subtract the translation vector (-2, 4) from the translated coordinates N'(5, -3), resulting in the coordinates N(7, -7).
Step-by-step explanation:
To find the coordinates of point N, we need to understand the translation that occurred when point M was moved to point M'. By comparing the coordinates M(-1,3) and M'(-3,7), we can determine the translation vector. The change in the x-coordinate is -3 - (-1) = -2, and the change in the y-coordinate is 7 - 3 = 4. This gives us the translation vector (-2, 4).
Applying the same translation to point N' to find the original point N, we simply reverse the translation. Since N' has coordinates (5,-3), subtracting the translation vector gives us the coordinates of N. The new x-coordinate is 5 - (-2) = 7, and the new y-coordinate is -3 - 4 = -7.
Therefore, the coordinates of point N are (7, -7).