Final answer:
Without the scale factor, it is not possible to determine the ordered pair for point G' after the dilation of polygon EFGH.
Step-by-step explanation:
If polygon EFGH is dilated by a scale factor to create polygon E'F'G'H', the new position of point G (which is G') can be determined by multiplying the original coordinates by the scale factor. Given that the original coordinate of point G is (-2,6), we need the scale factor to calculate the new coordinate. Since the scale factor is not provided in the question, we cannot determine the ordered pair for point G'.