Final answer:
The scale factor of the dilation from point A at (-3, 4) to point A' at (-9, 12) is 3, as both the x and y coordinates of A' are three times those of A.
Step-by-step explanation:
The question involves finding the scale factor of a dilation in geometry. The original point A is at (-3, 4), and the image point A' is at (-9, 12) after dilation. To find the scale factor, we compare the coordinates of A' to A.
We can set up the following proportion using the x-coordinates of A and A':
Scale factor = A'x / Ax
Substituting the given values into the proportion gives us:
Scale factor = (-9) / (-3)
= 3
Similarly, we could use the y-coordinates:
Scale factor = A'y / Ay
Scale factor = 12 / 4
= 3
Both proportions have given us the same scale factor of 3, indicating that the image A' is three times larger than the pre-image A in both the x and y directions.