8 -7 -6 -5 -4 -3 -2 -10 -1- -2- -3- -4- XY -5- -6- -7- -8- Z Y < (1 point) < Which statement proves that the dilation of AXYZ does not pass through the center of dilation? X'(-3-1/3,-3-1/3)=X'(-1,-1), Y'(-3-1/3,-6-1/3)=Y'(-1,-2), Z'(-6-1/3,-3-1/3)=2'(-2,-1). XY and XY' 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. OXY has a length of 3 and XY' has a length of 1, which proves that AXY'Z' is a dilation of AXYZ by a scale factor of 13. Responses XY has a length of 3 and X'Y' has a length of 1, which proves that AXYZ is a dilation of AXY'Z' by a scale factor of 3.

Answer 1

To determine which statement proves that the dilation of AXYZ does not pass through the center of dilation, we can analyze the information given regarding the slopes and relationships of the lines.

1. The statement about slopes indicates that lines XY and XY' both have an undefined slope with the center of dilation at (0, 0). This implies that both lines are vertical. If the dilation's center is indeed at (0, 0) and lines are parallel (both lines being vertical), then it indicates that the points are moving along lines that do not intersect the dilation center, confirming that the dilation does not pass through the center.

2. On the other hand, the response mentioning the lengths (XY has a length of 3 and XY' has a length of 1, indicating a scale factor of 1/3) also supports dilation, but does not necessarily prove that it doesn’t pass through the center of dilation.

Therefore, the most compelling statement that proves the dilation does not pass through the center of dilation is:

"XY and XY' 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 effectively indicates the nature of the relationship between the dilated lines and the center of dilation.