Answer:
The value of the scale factor (k) for the dilation is (A) k = 2.
Step-by-step explanation:
In a dilation, the coordinates of the image are obtained by multiplying the coordinates of the original point by the scale factor. Given that the image of the point (2, 3) is (8, 12), we can determine the scale factor (k) by comparing the corresponding coordinates: 8=2×k8=2×k and 12=3×k12=3×k. Solving these equations, we find that k=4k=4. Therefore, option C. k = 4 is the correct answer.
Understanding the relationship between the original and image coordinates in a dilation is fundamental. The scale factor represents the factor by which the original coordinates are multiplied to obtain the image coordinates. In this case, a scale factor of 4 correctly transforms (2, 3) to (8, 12).
Option A is correct.