Final answer:
By analyzing the relationship between original and dilated square coordinates, it is determined that point C(-3, 4) is the center of dilation where lines connecting corresponding points of the squares meet. Thus, the answer is (d) C.
Step-by-step explanation:
The student is tasked with determining which of the given points A, B, C, or D is the center of dilation when square WXYZ is dilated by a scale factor of 3 to create square W'X'Y'Z'. To find the center of dilation, we must determine which point, when connected to corresponding vertices of the two squares, shows that the lines are all concurrent (intersect at a single point) and that the distances from this point to corresponding vertices of each square are proportional according to the scale factor.
By comparing the coordinates of corresponding points of the original and dilated squares, it becomes apparent that each point of the dilated square is exactly 3 times farther away from a fixed point compared to the corresponding point on the original square. For instance, the dilation takes W(-4, 3) to W'(-6, 1). To find the scale factor between these two points, along the x-axis we have – (-6 + 4) / (-4 + 4) = 2 / 0, which is undefined, indicating a vertical dilation line; along the y-axis we have (1 - 3) / (3 - 3) = -2 / 0, which is also undefined, again indicating a vertical dilation line.
Following this method for other corresponding points, we would find that the lines connecting corresponding vertices would all pass through point C, therefore, point C(-3, 4) is the center of dilation. The lines W to W', X to X', Y to Y', and Z to Z' all intersect at C, which confirms that C is the center. Hence, the correct answer is (d) C.