Question

Square wxyz was dilated by a scale factor of 3 to create square w²x²y²z². Which point is the center of dilation?

1) b
2) a
3) d
4) c

Answer 1

The center of dilation is point A. Option 2 is correct.

Step-by-step explanation:

Dilation involves enlarging or reducing a figure by a certain scale factor from a center point. In this case, square WXYZ was dilated by a scale factor of 3 to form square W²X²Y²Z². Point A in square WXYZ corresponds to the same point in square W²X²Y²Z². Since the scale factor is 3, point A serves as the center of dilation. When a figure is dilated, corresponding points from the original figure to the new one are equidistant from the center of dilation, preserving the proportional increase or decrease in size.

Points B, C, and D in the original square WXYZ do not maintain the same relative positions in the dilated square W²X²Y²Z², indicating that they are not the center of dilation.

Therefore, point A, which remains unchanged during the dilation process and maintains its position as the corresponding point, is the center of dilation for the transformation from square WXYZ to square W²X²Y²Z².

Correct answer: 2) a