The statement that proves that the dilation of triangle \( \Delta XYZ \) does not pass through the center of dilation is:
"XY¯¯¯¯¯¯¯¯ and X′Y′¯¯¯¯¯¯¯¯¯¯¯¯ both have an undefined slope with a center of dilation at (0,0). This proves that the lines are parallel and that the dilation does not pass through the center of dilation."
This statement is relevant because, in a dilation, if the segments connect the pre-image and the image points through the center of dilation, they would not be parallel. Since both segments have an undefined slope (indicating they are vertical), they are parallel and therefore confirm that the dilation does not pass through the center of dilation.